Question

An ap consists of 37 terms the sum of the three middle most term is 225 and the sum of the last term is 429 find the ap 8

Answer 1

The AP has 37 terms.

The middle term is the 19th term.

So the sum of the middle three terms = (a+17d)+(a+18d)+(a+19) = 225, or

3a + 54d = 225, or

a+18d = 75 …(1)

So the sum of the last three terms = (a+34d)+(a+35d)+(a+36) = 429, or

3a+105 = 429, or

a + 35d = 143 …(2)

Subtract (1) from (2)

17d = 143–75 = 68, or d = 68/17 = 4.

From (1), a = 75–18d = 75–72 = 3.

So the first term of the AP is 3 and the cd = 4. The AP is thus: 3,7,11,15,…