Question

if the sum of 3rd and 8th term of an ap is 7 and the sum of 7th and 14th term is-3 find the 10th term​

Answer 1

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Answer 2

Answer:-

Given:

Sum of 3rd & 8th terms of an AP = 7

Sum of 7th & 14th terms = - 3

We know that,

nth term of an AP – a(n) = a + (n - 1)d

Hence,

⟶ a + (3 - 1)d + a + (8 - 1)d = 7

⟶ 2a + 2d + 7d = 7

⟶ 2a + 9d = 7 -- equation (1)

Similarly,

⟶ a + (7 - 1)d + a + (14 - 1)d = - 3

⟶ 2a + 6d + 13d = - 3

⟶ 2a + 19d = - 3 -- equation (2)

Subtract equation (1) from (2).

⟶ 2a + 19d - (2a + 9d) = - 3 - 7

⟶ 2a + 19d - 2a - 9d = - 10

⟶ 10d = - 10

⟶ d = - 10/10

⟶ d = - 1

Substitute the value of d in equation (1).

⟶ 2a + 9(- 1) = 7

⟶ 2a - 9 = 7

⟶ 2a = 7 + 9

⟶ 2a = 16

⟶ a = 16/2

⟶ a = 8

Now,

10th term – a(10) = 8 + (10 - 1)(- 1)

⟶ a(10) = 8 - 9

⟶ a(10) = - 1

Therefore, the 10th term of the given AP is - 1.