Question

The 9th
term of an AP is 449 and 448th term is 9. Find the 458th term of the A.P.​

Answer 1

Answer:-

Given:

9th term of an AP (a₉) = 449

448th term of an AP (a₄₄₈) = 9.

We know that;

nth term of an AP (aₙ) = a + (n - 1)d

Hence;

a₉ = a + (9 - 1)d

⟹ 448 = a + 8d

⟹ 448 - 8d = a -- equation (1).

Similarly;

⟹ a + (448 - 1)d = 9

⟹ a + 447d = 9

Substitute the value of a from equation (1).

⟹ 448 - 8d + 447d = 9

⟹ 439d = 9 - 448

⟹ 439d = - 439

⟹ d = - 439/439

⟹ d = - 1

Substitute the value of d in equation (1).

⟹ a = 448 - 8d

⟹ a = 448 - 8( - 1)

⟹ a = 448 + 8

⟹ a = 456

Now;

458th term of the AP (a₄₅₈) = a + 457d

⟹ a₄₅₈ = 456 + 457( - 1)

⟹ a₄₅₈ = 456 - 457

⟹ a₄₅₈ = - 1

∴ The 458th term of the given AP is - 1.