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The sum of 18 numbers of an AP is 234 and the sum of 26 terms is 442. What is the nth...

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The sum of 18 numbers of an AP is 234 and the sum of 26 terms is 442. What is the nth term of the series.

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The sum of 18 terms of an AP is 234 and the sum of 26 terms is 442. For an arithmetic series with first term a and common difference d, the nth term `T_n = a + (n - 1)*d` and the sum of the first n terms is `S_n = (n/2)*(2a + (n-1)*d)`

Here, the sum of the first 18 terms is 234.

=> 9*(2*a + 17*d) = 234

=> 2a + 17d = 26 ...(1)

And the sum of the first 26 terms is 442

=> 13*(2a + 25d) = 442

=> 2a + 25d = 34 ...(2)

From (1) and (2)

8d = 8

=> d = 1

a = 4.5

The nth term of the series is `T_n = 4.5 + (n - 1)`

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