If the sum of first 14 terms of an A.P. is 1050 and its first term is 10, find the 20^th term.
OR

The first term of an A.P. is 5, the last term is 45 and sum is 400. Find the number of terms and common difference.

Question

Philoid · Accepted Answer

First term = a = 10

S₁₄ = 1050

To find: 20^th term.

⇒ 20 + 13d = 150

⇒ d = 10

So, a₂₀ = a + 19d = 10 + 190 = 200

Thus, the 20^th term is 200.

OR

Number of terms = 16, Common difference

First term = a = 5, Last term = a_l = 45, Sum = 400

Last term = a + (n – 1) d = 5 + (n – 1) d = 45

⇒ (n – 1) d = 40 … (1)

⇒ n = 16

So, (16 – 1) d = 40

If the sum of first 14 terms of an A.P. is 1050 and its first term is 10, find the 20th term.ORThe first term of an A.P. is 5, the last term is 45 and sum is 400. Find the number of terms and common difference.