CAT 2005 — QA Question 14
Miscellaneous ProgressionsEasy
Passage / Data
Answer the next 2 questions based on the information given below.
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.
If a1 = 1 and an + 1 – 3an + 2 = 4n for every positive integer n, then a100 equals
Answer & solution
- A
399 – 200
- B
399 + 200
3100 – 200
- D
3100 + 200
Solution
a1 = 1
an+1 = 4n + 3an – 2
a2 = 4 + 3(1) – 2 = 5 = 32 – 4
a3 = 4(2) + 3(5) – 2 = 21 = 33 – 6
a4 = 4(3) + 3(21) – 2 = 73 = 34 – 8
∴ an = 3n – 2(n)
∴ a100 = 3100 – 200
Hence, option (c).