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# The seconds term of a geometric series is 4 while the fourth term is 16. Find th...

### Question

The seconds term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms

A) 60

B) 62

C) 54

D) 64

### Explanation:

T2 = 4, T4 = 16
Tx = arn-1
T2 = ar2-1 = 4 i.e. ar3 = 16, i.e. ar = 4
T4 = ar4-1
therefore, $$\frac{T_4}{T_r}$$ = $$\frac{ar^3}{ar}$$ = $$\frac{16}{4}$$
r2 = 4 and r = 2
but ar = 4
a = $$\frac{4}{r}$$ = $$\frac{4}{2}$$
a = 2
Sn = $$\frac{a(r^n - 1)}{r - 1}$$
S5 = $$\frac{2(2^5 - 1)}{2 - 1}$$
= $$\frac{2(32 - 1)}{2 - 1}$$
= 2(31)
= 62

## Dicussion (1)

• T2 = 4, T4 = 16
Tx = arn-1
T2 = ar2-1 = 4 i.e. ar3 = 16, i.e. ar = 4
T4 = ar4-1
therefore, $$\frac{T_4}{T_r}$$ = $$\frac{ar^3}{ar}$$ = $$\frac{16}{4}$$
r2 = 4 and r = 2
but ar = 4
a = $$\frac{4}{r}$$ = $$\frac{4}{2}$$
a = 2
Sn = $$\frac{a(r^n - 1)}{r - 1}$$
S5 = $$\frac{2(2^5 - 1)}{2 - 1}$$
= $$\frac{2(32 - 1)}{2 - 1}$$
= 2(31)
= 62