Sequences

explicit form

explicit form

nth term is found using n as the only variable (xn= 2n: 2, 4, 6,…)

recursive form

describes nth term using previous terms (xn= xn-1 + xn-2 for n>= 3 x1= 1 and x2= 1: 1, 1, 2, …)

series

sum of terms of a sequence, sequence has an nth term formula

sigma notation - up

ending term number (not the actual value)

sigma notation - middle

explicit formula for nth term

sigma notation - down

starting term number (first value you plug in for n eg. 1)

arithmetic sequence

add or subtract

arithmetic sequence - recursive formula

an = an-1 + d ( where d is the common difference)

arithmetic sequence - explicit formula

an= a1 + (n-1)d (d is common difference)

sum of arithmetic sequence

(2a1 + (n-1)d) x n/2 or (a1 + an)n/2

geometric sequence

multiply or divide

geometric sequence - recursive formula

gn = gn-1 x r (r is the common ration)

geometric sequence - explicit formula

gn = g1 x r^n-1 (r is the common ration)

sum of terms of geometric sequence

g1(r^n - 1)/ r-1 (if n is infinite than n=0)

financial word problem - n

the number of payments

financial word problem - 1%

the interest by percentage

financial word problem - PV

present value

financial word problem - PMT

periodic payment

financial word problem - FV

future/final value

financial word problem - P/Y and C/Y

payments per year and times per year interest is compounded (same value)

find nth term - calculator

1. Mode

2. SEQ

3. plug in formula

4. use variable buttons