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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

Options

A) 60

B) 62

C) 54

D) 64

The correct answer is B.

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

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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

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