PrepRung
Sign inSign up free

JEE Main 2017 · Mathematics · Sequences and Series · easy

The sum of an infinite geometric series is 6 and its first term is 3. The second term is

Single correct option

The sum of an infinite geometric series is 66 and its first term is 33. The second term is
  1. A. 11
  2. B. 22
  3. C. 32\frac{3}{2}
  4. D. 34\frac{3}{4}
Show answer and solution

Answer: (C) 32\frac{3}{2}

For an infinite GP with first term aa and ratio rr, S∞=a1−rS_\infty=\dfrac{a}{1-r}. So 6=31−r6=\dfrac{3}{1-r} gives 1−r=121-r=\dfrac12, hence r=12r=\dfrac12. The second term is ar=3⋅12=32ar=3\cdot\dfrac12=\dfrac32, and ∣r∣<1|r|<1 confirms convergence.
Report a mistake

Original question written in the JEE Main 2017 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake