A man saves ₹ 145000 in ten years. In each year after the first year. he saved ₹ 2000 more than he did in the proceeding year. How much did he save in the first year?

Let the man first save ₹ P in the first year.
Then, the given sequence is P + (P + 2000) + (P + 4000) + ..,
which is an AP with a = P , d = (P + 2000) - P = 2000,
n = 10, S_n = 145000
S_n = n/2[2a + (n - 1)d]
⇒ 145000 = 10/2 [2 x P + 9 x 2000] = 5 [2P + 18000]
⇒ 2P + 18000 = 145000/5 = 29000
⇒ 2P = 29000 - 18000
⇒ 2P = 11000
∴ P = ₹ 5500
So, the man save ₹ 5500 in the first year .