Q. 205.0( 5 Votes )

Which term of the A.P. 3, 10, 17, 24, ... will be 84 more than its 13th term ?

Answer :

Given: 3, 10, 17, 24, ...


First we need to calculate 13th term.


We know that


an = a + (n – 1)d


Here, a = 3, d = 10 – 3 = 7 and n = 13


So, a13 = 3 + (13 – 1)7


a13 = 3 + 12 × 7


a13 = 3 + 84


a13 = 87


Now, the term is 84 more than a13 is 84 + 87 = 171


Now,


a + (n – 1)d = 171


3 + (n – 1)7 = 171


3 + 7n – 7 = 171


7n = 171 + 7 – 3


7n = 175


n = 25


Hence, the 25th term is 84 more than the 13th term.


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