3. SEQUENCE, SERIES & PROGRESSION

Determine the sum of the first 4 terms of the sequence whose general term is given by 3^n - 2

112

Determine the 5th term of the sequence whose sum of n terms is given by 2^(n + 3) - 5

471

Find the 20th term of the progression 4,9,14,19,... and also, it's sum.

99, 1030

How many terms of the progression 3,5,7,... must be in order that their sum will be 2600?

50

In the recent "Gulf War" in the Middle East, the Allied Forces captured 6400 of Saddam's soldiers and with provisions on hand that will last for 216 meals while feeding 3 meals per day. The provision lasted 9 more days because of daily deaths. At an average, how many died per day?

-17.78

A besieged fortress is held by 5700 men who have provisions for 66 days. If the garrison loses 20 men each day, for how many days can the provision hold out?

76

A Geodetic engineering student got a score of 30% on Test 1 of the five-number test in Surveying. On the last number, he got 90% in which a constant difference more on each number than he had on the immediately preceding one. What was his average score in surveying? ____ %

60

A small line truck hauls poles from a substation stockyard to pole sites along a proposed distribution line. The truck can handle only one pole at a time. The first pole is 150 m from the substation, and the poles are to be 50m apart. Determine the total distance traveled by the truck back and forth after returning from delivering the 30th pole in meters.

52500

If the 5th term of an arithmetic progression is 17 and the 3rd term is 10. Find the 30th term of the sequence and its sum.

104.5 , 1612.5

There are 4 geometric means between 3 and 729. Find the fourth term of the geometric progression.

81

A country has a billion-dollar paper currency. The bank clearing consisting of old and new currency, amounts to 5M dollars per day. The government decides to introduce a new currency, all old paper currency coming into the banks are being exchanged for new. How long will it take for the currency in circulation to become 90% new?

460

In a benefit show, a number of wealthy men agreed that the first one to arrive would pay 10 centavos to enter and each later arrival would pay twice as much as the preceding man. The total amount collected from all of them was Php 104, 857.50. How many wealthy men paid?

20

If the sum of the terms in geometric progression is 1820. How many terms are there if the first term is 5, the second term is 15 and the third term is 45?

6

A body dropped from a height of 16m during the first second, 48m in the next second, 144m on the third second and so on. Find how far the body falls during the 7th second and the total distance travelled.

11664, 17488

If one third of the air in the tank is removed by each stroke of an air pump, what fractional part of the total part of the air is removed in 6 strokes.

665/729

The number of bacteria in a certain culture doubles every 3 hours. If there are 10 bacteria initially, find the number of bacteria in 24 hours.

2560

If a stroke of a vacuum pump removes 10% of the air from the container, how much of the original air remains after 10 strokes?

0.34868

A rubber ball is made to fall from the height of 50ft and is observed to rebound 2/3 of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner? __ ft

250

Find the total distance travelled by the tip of a pendulum if the distance of the first swing is 6cm and the distance of each succeeding swing is 0.98 of the distance of the previous swing. ____ cm

Find the harmonic mean between 1/2 and 1/8.

1/5

The 6th term of a harmonic progression is 12 and the 10th term is 6, find the 18th term.

3

Determine the harmonic mean between a and b.

3

The geometric mean and arithmetic mean of the two numbers are 8 and 17, respectively.
a) Find the bigger number

b) Find the smaller number

c) Find the harmonic mean

32, 2, 64/17

If the sum is 220 and the first term is 10, find the common difference if the last term is 30.

2

The mean of x and y is a, the mean of y and z is b, and the mean of x and z is c. What is the mean of x, y, and z?

(a + b + c)/3

The arithmetic mean of 80 numbers is 55. If two numbers namely 250 and 850 are removed, what is the arithmetic mean of the remaining numbers?

550/13

The arithmetic mean of 6 numbers is 17. If two numbers are added to the progression, the new set of numbers will have an arithmetic mean of 19. What are the two numbers if their difference is four?

23, 27

The arithmetic mean of a and b is

(a + b)/2

The sum of three arithmetic means between 34 and 42 is

114

Gravity causes a body to fall 16.1 ft. in the first second, 48.3 in the 2nd second, 80.5 in the 3rd second. How far did the body fall during the 10th second? _____ ft

305.9

If the first term of an arithmetic progression is 25 and the fourth term is 13, what is the third term?

17

What is the sum of the progression 4, 9, 14, 19... up to the 20th term?

1030

A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer, and so on until there are 10 bricks in the last layer. How many bricks are there all together?

639

Determine the sum of the progression if there are 7 arithmetic mean between 3 and 35

171

Once a month, a man puts some money into the cookie jar. Each month, he puts 50 centavos more into the jar than the month before. After 12 years, he counted his money; he had P 5,436. How much money did he put in the jar in the last month?

73.5

In a pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there?

14

Find the 30th term of the arithmetic progression 4, 7, 10...

91

A girl on a bicycle coast downhill covering 4 feet the first second 12 feet the second, and in general, 8 feet more each second than the previous second. If she reaches the bottom at the end of 14 seconds, how far did she

When all odd numbers from 1 to 101 are added, the result is

How many times will a grandfather's clock strikes in one day if it strikes only at the hours and strike once at 1 o'clock, twice at 2 o'clock, thrice at 3 o'clock ad so on?

To conserve energy due to the present energy crisis, the Meralco tried to readjust their charges to electrical energy users who consumes more than 2000 kw-hours. For the first 100 kw-hr, they charged 40 centavos and increasing at a constant rate more than the preceding one until the fifth 100 kw-hr, the charge is 76 centavos. How much is the average charge for the electrical energy per 100 kw-hr?

The 3rd term of a harmonic progression is 15, and the 9th term is 6. Find the 11th term

Find the fourth term of the progression 1/2, 0.2, 0.125

23. Find the 9th term of the harmonic progression 3, 2, 3/2...

Find the sum of 4 geometric means between 160 and 5

The fourth term of a geometric progression is 216, and the 6th term is 1944. Find the 8th term

Determine x so that: x, 2x + 7, 10x-7 will be a geometric progression

A product has a current selling of P 325.00. If its selling price is expected to decline at the rate of 10% per annum because of obsolescence, what will be its selling price four years hence?

The number 28, x + 2, 112 form a geometric progression. What is the 10th term?

The sum of the first 10 terms of a geometric progression 2, 4, 8... is

A person has 2 parents, 4 grandparents, 8 great-grandparents, and so on. How many ancestors are there during the 15 generations preceding his own, assuming no duplication?

65534

If the first term of a geometric progression is 9 and the common ratio is -2/3, find the fifth

The seventh term is 56 and the twelfth term is -1792 of a geometric progression. Find the common ratio and the first term. Assume the ratios are equal.

-2, 7/8

In the PBA three-point shootout contest, the committee decided to give a prize in the following manner, A prize of P 1 for the first basket made, P 2 for the second, P 4 for the third, P 8 for the fourth and so on. If the contestant wants to win a prize no less than a million pesos, what is the minimum number of baskets to be converted?

A man mailed 10 chain letters to ten of his friends with a request to continue by sending a similar letter to each of their ten friends. If this continue for 6 sets of letters and if all responded, how much will the Phil. Postal office earn if minimum postage costs P 4 per letter?

Determine the sum of the infinite series s = 1/3+1/9+1/27+...+ (1/3)^n

1/2

Under favorable condition, a single cell bacteria divided into two about every 20 minutes. If the same rate of division is maintained for 10 hours, how many organisms is produced from a single cell?

A rubber ball is made to fall from a height of 50 feet and is observed to rebound 2/3 of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner?

Find the sum of the infinite geometric progression 6, -2, 2/3...

Find the sum of 1, -1/5, 1/25...

Find the ratio of an infinite geometric progression if the sum is 2 and the first term is 1/2

If equal spheres are piled in the form of a complete pyramid with an equilateral triangle as base, find the total number of spheres in the pile if each side of the base contains 4 spheres.0

Find the 6th term of the sequence 55, 40, 28, 19, 13....

In the series 1, 1, 1/2, 1/6, 1/24... determine the 6th term