GMAT Quant Question Bank | Sum of GP Q20

GMAT Sample Questions | Geometric Progression

The GMAT Math practice question given below is a sequences and series question. Concept covered is sum of a Geometric Progression and its common ratio and working with algebraic identities. A medium difficulty GMAT 650 level problem solving question.

Question 20: If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 9, what is the common ratio of the G.P?

1. 3
2. $$frac {1} {3}$ 3. 2 4. 9 5. $\frac {1} {9}$ Get to Q51 in GMAT Quant Online GMAT Course @ INR 3500 Video Explanation GMAT Live Online Classes Starts Tue, Aug 17, 2021 Explanatory Answer Step 1 of solving this GMAT Geometric Progressions question: Formula to find the sum of first 'n' terms of a GP The sum of the first n terms of a G.P. is given by $\frac {{{ar}^{n}}-a} {r-1}$, where 'a' is the first term of the G.P., 'r' is the common ratio and 'n' is the number of terms in the G.P. Therefore, the sum of the first 6 terms of the G.P will be equal to $\frac {a\left${r}^{6}-1$right$} {r-1}) And sum of the first 3 terms of the G.P. will be equal to $\frac {a\left$ r^3-1$right$} {r-1}) Step 2 of solving this GMAT Geometric Progressions question: Use the ratio between these two sums to find 'r' The ratio of the sum of the first 6 terms : sum of first 3 terms = 9 : 1 i.e. $\frac {\frac {a\left$r^6 - 1$right$} {r - 1}} {$frac {a\left$r^3 - 1$right$} {r - 1}}) = 9 $\frac {{{r}^{6}}-1} {{{r}^{3}}-1}$ = $\frac {\left$ {{{r}^{3}}+1} $right$$left$ {{{r}^{3}}-1} $right$} {{{r}^{3}}-1}) = 9 Or r3 + 1 = 9 r3 = 8 r = 2 Choice C is the correct answer. GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! Already have an Account? GMAT Live Online Classes Next Batch Aug 17, 2021 GMAT Coaching in Chennai Next Batch after Lockdown GMAT Coaching in Chennai Sign up for a Free Demo of our GMAT Classes in Chennai Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India How to reach Wizako? Phone:$91) 44 4500 8484
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