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The sum of the 2^{nd} and the 7^{th} terms of an AP is 30. If its 15^{th} term is 1 less than twice its 8^{th} term, find the AP.

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#### Solution

Solution:

The sum of 2^{nd} and the 7^{th} terms of an AP is 30

(a + d) + (a + 6 d) = 30

2a + 7d = 30 ..................(i)

Now,

15^{th} term is 1 less than twice the 8^{th} term

(a + 14d) = 2(a + 7d) -1

a + 14d = 2a + 14d -1

a = 1............................ (ii)

Substituting the values in (i)

2x1 + 7d = 30

d = 4............................ (iii)

Hence, the terms in AP are …. a, a+d, a+2d, a+3d….

AP : 1,5,9 ……

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