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CAT 2000 — QA Question 3

Geometric ProgressionEasy

If a1 = 1 and an+1 = 2an + 5, n = 1, 2 ... , then a100 is equal to

Answer & solution

  • A

    (5 × 299 – 6)

  • B

    (5 × 299 + 6)

  • C

    (6 × 299 + 5)

  • (6 × 299 – 5)

Solution

a1 = 1 = 6 – 5

a2 = 7 = 12 – 5 = 6 × 2 – 5

a3 = 19 = 24 – 5 = 6 × 22 – 5

a4 = 43 = 48 – 5 = 6 × 23 – 5

and so on.

Thus, a100 = 6 × 299 – 5

Hence, option (d).

CAT 2000 QA Q3: If a 1 = 1 and a n+1 = 2a n + 5, n = 1, 2 ... , then a 100 is equal to — Solution | TheCATExam