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nth Term of an AP

The sum of th...

Question

The sum of the $2^{r d}$ term and the $7^{t h}$ term of an A. P. is 30. If its $15^{t h}$ term is 1 less than twice of its $8^{t h}$ term, find the A. P.

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Solution

Given

$a_{2} + a_{7} = 30 a + d + a + 6 d = 30 2 a + 7 d = 30 - - - - (1) a_{15} = 2 a_{8} - 1 a + 14 d = 2 (a + 7 d) - 1 a + 14 d = 2 a + 14 d - 1 a = 1 P u t i n (1) 2 (1) + 7 d = 30 7 d = 28 d = 4 A P : 1, 5, 9, 13, \dots$

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