Visual SolutionPYQ 2023 · Apr 10 Shift 1Standard

Question

Let the first term

a

and the common ratio

r

of a geometric progression be positive integers. If the sum of squares of its first three terms is

33033

, then the sum of these three terms is equal to

(A)

241

(B)

231

(C)

210

(D)

220

Solution Path

a^2(1 + r^2 + r^4) = 33033

. With

r = 4

a = 11

. Sum

= 11(21) = 231

01Question Setup

1/4

GP with positive integer

a

and

r

. Sum of squares of first 3 terms is

33033

. Find the sum.

a + ar + ar^2 = \;?

02Set Up Equation

2/4

a^2(1 + r^2 + r^4) = 33033

. Since

a, r

are positive integers, try values of

r

a^2(1 + r^2 + r^4) = 33033

03Find a and rKEY INSIGHT

3/4

Try

r = 4

1 + 16 + 256 = 273

. Then

a^2 = 33033/273 = 121

, so

a = 11

. Sum

= 11(1 + 4 + 16) = 231

11 \times 21 = 231

04Final Answer

4/4

Sum of three terms

= 231

\boxed{231}

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