Answer :

The nth term of an A.P. with first term as and common difference as d is given by,

an = a + (n – 1) d


a2 = a + d


a7 = a + 6d


According to question,


a2 + a7 = 30


a + d + a + 6d = 30


2a + 7d = 30 …. (i)


a15 = a + 14d


a8 = a + 7d


According to question,


a15 = 2a8 – 1


a + 14d = 2 (a + 7d) – 1


a + 14d = 2a + 14d – 1


a = 1


Substituting the value of a in eq (i), we get


d = 4


The terms of the A.P. are 1, 5, 9, 13, 17, 21, …., nth


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