Mathematics

If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find…

If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first for term

  • A.
    -45
  • B.
    -15
  • C.
    15
  • D.
    33
  • E.
    45
Correct Answer: Option E
Explanation

T(_{2}) = ar = 6

T(_{5}) = ar(^{4}) = 48

(frac{T_5}{T_2}) = (frac{ar^{4}}{ar}) = (frac{48}{6})

= r(^{3}) = 8

⇒ r = 2

S(_{n}) = (frac{a((r^n) – 1)}{r – 1})

S(_{4}) = (frac{a((r^4) – 1)}{r – 1})

S(_{4}) = (frac{3((2^4) – 1)}{2 – 1})

= 3(16 -1)

= 45