Question

The fourth term of an exponential sequence is 108 and the ratio is 3 . Calculate the value of the eighth term of the sequence, calculate the sum of the first five terms of the sequence.

Answer 1

8th term = 8748 , Sum of 5 terms = 484

Explanation:

Formula for nth term in an exponential sequence = a r^ (n-1)

Here : n = 4 , ratio r = 3 ; And nth ie 4th number = 108

So, a r^ (n-1) = nth item implies that → a 3 ^ (4-1) = 108

a 3^3 = 108 → 27 a = 108 → a = 108 / 27 → a = 4

8th term = a r^ (n-1) , at n = 8. So, = 4 3^(8-1) = 4 3^7 = 4 x 2187 = 8748

Sum of n terms = a [(r^n) -1 ] / [r - 1] → Sum 5 terms = 4 [ (3^5)- 1] / [3 - 1]

= 4 [ (243) - 1] / 2 ] = 2 x 242 = 484