If the 10th term of the sequence a, a - b, a - 2b, a - 3b,......is 20 and the 20th term is 10, then the x^th term of the series is

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Bihar Police Constable Memory Based Paper (Held On: 1st October 2023 Shift 1)

Answer 1

Given:

The 10th term of the sequence a, a - b, a - 2b, a - 3b,......is 20. The 20th term is 10.

Calculation:

10^th term = a - 9b = 20 --(1)

20^th term = a - 19b = 10 ---(2)

On subtracting equation (2) from (1):

a - 9b - (a - 19b) = 20 - 10

⇒ a - 9b - a + 19b = 10

⇒ 10b = 10

⇒ b = 1

From equation (1):

a - 9 (1) = 20

⇒ a = 20 + 9 = 29

Now, x^th term = a - (x - 1)b

⇒ 29 - (x - 1) (1)

⇒ 29 - x + 1 = 30 - x

∴ The xth term of the sequence is 30 - x.

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