What is the sum of a 6-term geometric series if the first term is 24 and the last term is 1,417,176?

First, we need to solve for the common ratio from the data given by using the equation.

a(n) = a(1) r^(n-1)
1417176 = 24 r^(6-1)
59049= r^5
r = 9

We can find the sum by the expression:

 S(n) = a(1) ( 1 - r^n) / 1-r

where a(1) is the first term, r is the ratio and n is the number of terms.

S(9) = 24 (1 - 9^6) / 1-9
S(9) = 1594320

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2