Question

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

Answer 1

AP = 3, 10, 17, ....

First term = 3

Common Difference = 7

Number of terms ( x ) = ?

Aₓ = 84

Formula : Aₓ = a + ( x - 1 ) d

=> 84 = 3 + ( x - 1 ) 7

= 84 - 3 = ( x - 1) 7

=> 81 = ( x - 1 ) 7

=> 81 / 7 = x - 1

=> 11.57 = x - 1

=> x = 11.57 + 1 = 12.57

Since the number of term is close to 12.5 we can say that 84 is a term which is close to 13th term and it lies between 12th and 13th term.