Question

What is the formula for geometric progression???

Answer 1

2,x, 32 are in GPGP progression isa, ar, ar^2....a = 2 ....(1)ar^2 = 32 ....(2)Using equation 1 and 22r^2 = 32r^2 = 16r=±4Hence,x = ar = 2*±4 = ±8Hence proved ,1,1/3,1/9,-1/27,…… Infinity .sum to infinitySum = a(1-r^n)/(1-r)Sum_infinity = a/1-rSum_infinity = 1/(1-(-1/3)Sum_infinity = 1/(1+1/3)Sum_infinity = 1/(4/3)Sum_infinity = 3/4

Answer 2

To find the nth term of a geometric sequence we use the formula:

where r common ratio

a1 first term

an-1 the term before the n th term

n number of terms

Sum of Terms in a Geometric Progression

Finding the sum of terms in a geometric progression is easily obtained by applying the formulas:

nth partial sum of a geometric sequence

sum to infinity

where Sn sum of GP with n terms

S∞ sum of GP with infinitely many terms

a1 the first term

r common ratio

n number of terms