Question

An AP consists of 29 terms. The sum of 3-middle most terms is 375 and the sum of the last

3terms is 531. Find the AP.​

Answer 1

Answer:

The AP is 69, 77, 81, 85..

with a = 69, d = 4

Step-by-step explanation:

The AP consists of 29 terms.

Therefore, the middle most term is the 15th term.

Given,

a(14) + a(15) + a(16) = 375

a(1) + 13d + a(1) + 14d + a(1) + 15d = 375

3a(1) + 42d = 375

a(1) + 14d = 125 ---(1)

and, a(27) + a(28) + a(29) = 531

a(1) + 26d + a(1) + 27d + a(1) + 28d = 531

3a(1) + 81d = 531

a(1) + 27d = 177 ---(2)

Subtracting eq 1 from eq 2,

13d = 52

d = 4

Substituting d=4 in eq 1,

a(1) + (14×4) = 125

a(1) = 125 - 56 = 69

a(1) = 69

a(2) = a(1) + d = 69 + 4 = 73

a(3) = a(1) + 2d = 69 + (4×2) = 69 + 8 = 77

a(4) = a(1) + 3d = 69 + (4×3) = 69 + 12 = 81

a(5) = a(1) + 4d = 69 + (4×4) = 69 + 16 = 85

The AP is 69, 77, 81, 85..