Question

An AP which has 21 terms, the sum of three middle terms (i.e. the number before and after of median and median itself) is 726 and the sum of last three terms is 1320. Then what is the value of 17^th term?
1. 300
2. 475
3. 478
4. 374
5. 574

Answer 1

Correct Answer - Option 4 : 374

Given:

Sum of three middle terms = 726

Sum of last three terms = 1320

Formula used:

a_n = a + (n – 1)d

Concept:

Using the concept of linear equation we can find the value of 17^th term.

Calculation:

Middle terms of the given AP must be 10^th, 11^th and 12^th

As the numbers will of same difference

∴ Average of these terms (i.e., 11^th term) = 726/3 = 242   ----(i)

Similarly, last three terms must be 19^th, 20^th and 21^st

 ∴ Average of last three terms (i.e., 20^th term) = 1320/3 = 440   ----(ii)

Now, a₁₁ = a + 10 d and a₂₀ = a + 19d

⇒ 242 = a + 10d [From (i)]   ----(iii)

⇒ 440 = a + 19d [From (ii)]   ----(iv)

By using elimination method of linear equation in two variables, solve equations (iii) and (iv)

Then, we get d = 22 and put the value of d in equation (iii) then we get a = 22

Now, we have the value of a and d then we can easily find the 17^th term

⇒ a₁₇ = a + 16d

⇒ a₁₇ = 22 + 16 × 22

⇒ a₁₇ = 374

∴ 17^th term is 374