IPMAT Indore 2024 - QA (MCQ) Q31 Explanation

Explanation:

(b) Let the series be a, ar, ar2 …..

Given: Sum∞ = a/1−r = 80 …(i)

Also, a +ar = a(1 +r) = 35 …(ii)

⇒ 80(1 –r) (1 + r) = 35

⇒ 1 – 𝑟^2 = 35/80 = 7/16

⇒ 𝑟^2 = 9/16

⇒ r = ± 3/4

Substituting r = 3/4 in eq.(i) we get a = 20. These values of a and r, won’t lead the sum of series to 100 as sum of infinite terms is 80 only.

 Substituting r = −3/4 in eq.(i) we get a = 140.

a1= 140;

a2= 140 × −3/4 = −105;

a3 = −105 × −3/4 = 78.75 ;

a4 = − 78.75 × −3/4 = −59.0625;

a5 = −59.0625 × −3/4 = 44.296875 & so on.

Adding first 5 terms of the series, we get a1 + a2 + a3 + a4 + a5 = 98.984375 ≈ 100.

So, the sum of first 5 terms of the series when r = −3/4 and a = 140 gives the sum close to 100.