Mathematics
JAMB 2011
The seconds term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms
Correct Answer: Option B
Explanation
T
2 = 4, T
4 = 16
T
x = ar
n-1
T
2 = ar
2-1 = 4 i.e. ar
3 = 16, i.e. ar = 4
T
4 = ar
4-1
therefore, \(\frac{T_4}{T_r}\) = \(\frac{ar^3}{ar}\) = \(\frac{16}{4}\)
r
2 = 4 and r = 2
but ar = 4
a = \(\frac{4}{r}\) = \(\frac{4}{2}\)
a = 2
S
n = \(\frac{a(r^n - 1)}{r - 1}\)
S
5 = \(\frac{2(2^5 - 1)}{2 - 1}\)
= \(\frac{2(32 - 1)}{2 - 1}\)
= 2(31)
= 62
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