If an in-th term of the A.P. 5, 12, 19,.... then what is the value of a40 - a35 ?

Question

If \(a_n\) is n-th term of the A.P. 5, 12, 19,.... then what is the value of \(a_{40} -a_{35}\) ?

(A) 20

(B) 35

(C) 30

(D) 55

Answer 1

Correct option is (B) 35

The given A.P is \(5,12,19, \ldots\)

First term (a) = 5

Common difference (d) = 12 - 5 = 7

Now,

\(a_n =a+(n-1) d\)

\(\therefore a_{40} =5+(40-1) \times 7\)

\(=5+(39) \times 7\)

\(=5+273\)

\(=278\)

\(\therefore a_{35} =5+(35-1) \times 7\)

\( =5+(34) \times 7\)

\( =5+238\)

\(=243\)

\(\therefore a_{40}-a_{35} =278-243 \)

\(= 35\)