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The seconds term of a geometric series is 4 while the fourth term is 16….

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
Correct Answer: Option 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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