CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

The question is about Sum of infinite terms. First term and sum of the series is given and we need to find out the 4th term. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 13: Sum of infinite terms of a GP is 12. If the first term is 8, what is the 4th term of this GP?

1. \\frac{8}{27}\\)
2. \\frac{4}{27}\\)
3. \\frac{8}{20}\\)
4. \\frac{1}{3}\\)

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Progressions: What is the formula for infinite terms of a GP?

S_∞ = 12 and a = 8
S_∞ = \\frac{a}{1 - r}\\)
12 = \\frac{8}{1 - r}\\)
1 - r = \\frac{2}{3}\\)
r = \\frac{1}{3}\\)
Now t₄ = 8 * \\frac{1}{3}^{3}\\)
t₄ = \\frac{8}{27}\\)

The question is "Sum of infinite terms of a GP is 12. If the first term is 8, what is the 4th term of this GP?"

Hence the answer is "\\frac{8}{27}\\)"

Choice A is the correct answer.