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CAT 2019 Slot 2 — QA Question 5

Miscellaneous ProgressionsEasy

Let a1 , a2 be integers such that a1 - a2 + a3 - a4 + ........ + (-1)n-1 an = n , for n ≥ 1. Then a51 + a52 + ........ + a1023 equals

Answer & solution

  • A

    -1

  • 1

  • C

    0

  • D

    10

Solution

Given that a1 - a2 + a3 - a4 + ........ + (-1)n-1 an = n

Put n = 1 ⇒ a1 = 1

Put n = 2 ⇒ a1 - a2 = 2 ⇒ a2 = 1 - 2 = -1

Put n = 3 ⇒ a1 - a2 + a3 = 3 ⇒ a3 = 3 – 1 -1 = 1

Hence, the series proceeds as 1, -1, 1, -1, ...

i.e. odd term of the series = +1

& even terms of the series = -1

Then a51 + a52 + ........ + a1023 = 1 + (-1) + .... + 1

⇒ a51 + a52 + ........ + a1023 = 1

Hence, option (b).

CAT 2019 Slot 2 QA Q5: Let a 1 , a 2 be integers such that a 1 - a 2 + a 3 - a 4 + ........ + (-1) n-1 a n = n , for n ≥ 1. Then a — Solution | TheCATExam