Arithmetic Sequences

4

What is the common difference of the sequence 3, 7, 11, 15,...?

-29

Find u₂₀ for the sequence 9, 7, 5, 3, ...

610

Find the sum of the first 10 terms of the sequence 2, 5, 8, 11

200

The first term of an arithmetic sequence is 2 and the common difference is 4. Find the sum of the first 10 terms

-3

An arithmetic sequence has 15 terms. The first term is 30 and the last term is -12. Find the common difference

915

An arithmetic sequence has first term 12, and the third term is 26. Find the sum of the first 15 terms.

28

The sum of a sequence with 7th term -2 and 12th term 8 is 364. Find the number of terms in the sequence

11

Archie uses an exercise bike each time he goes to the gym. The first time he goes he uses the bike for 10 minutes. Each time he uses the bike he increases his time by 2 minutes. He aims to eventually use the bike for 30 minutes. After how many sessions will he manage the full 30 minutes?

220

Archie uses an exercise bike each time he goes to the gym. The first time he goes he uses the bike for 10 minutes. Each time he uses the bike he increases his time by 2 minutes. He aims to eventually use the bike for 30 minutes. How many minutes will he have spent on the bike in total when he reaches 30 minutes?

4100

Calculate 5 + 10 + ... + 195 + 200

117000

Priya has recently left university and started a job, so she is beginning to save money for a pension. She expects to save £1000 from her earnings in the first year, and then increase her annual savings by £200 so that in year 2 she will save £1200, in year 3 £1400, and so on. She intends to follow this plan for the next 30 years. How many pounds does she expect to save in total?

56

Fred has recently bought a new bathroom suite, at a cost of £2000 in total, including any interest payments. He chooses to pay using the supplier's 'easy

terms' Scheme A.

A: Pay £20 in the first month and then increase the payments by £4 every subsequent month.

In fact, the final month's payment is too much to cover the remaining debt. Calculate how much Fred should pay in the final month to clear his debt exactly. (hint work out how many months he'll be paying the bathroom off).