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

1 thought on “<br />The 9th<br />term of an AP is 449 and 448th term is 9. Find the 458th term of the A.P.​”

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.

   Reply