Q. 225.0( 1 Vote )

The sum of the 2<

Answer :

Given the sum of the 2nd and 7th terms of an AP is 30.


We know that the nth term of an AP, an = a + (n – 1) d.


a2 = a + (2 – 1) d = a + d


a7 = a + (7 – 1) d = a + 6d


As given, a + d + a + 6d = 30


2a + 7d = 30 … (1)


Also given 15th term is 1 less than twice its 8th term.


a15 = a + (15 – 1) d = a + 14d


a8 = a + (8 – 1) d = a + 7d


As given, a + 14d = 2 (a + 7d) – 1


a + 14d = 2a + 14d – 1


a - 1 = 0


a = 1


Substituting a = 1 in (1),


2a + 7d = 30


2 + 7d = 30


7d = 28


d = 4


Now, we got the first term, a = 1 and the common difference, d = 4,


The AP is as follows: 1, 5, 9, 13, …


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