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

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

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Solution

Solution:
The sum of 2nd and the 7th terms of an AP is 30
(a + d) + (a + 6 d) = 30
2a + 7d = 30 ..................(i)
Now,
15th term is 1 less than twice the 8th 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 ……

Concept: Arithmetic Progression
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