Question

Common difference of an Arithmetic Progression, whose 3^rd term is 5 and 7^th term is 9, is 

A) 1 

B) 2 

C) 3 

D) 4

Answer 1

Correct option is (A) 1

We have \(a_3=5\;\&\;a_7=9\)

\(\therefore a+2d=5\)   ______________(1)

& \(a+6d=9\)   ______________(2)    \((\because a_n=a+(n-1)d)\)

Subtract equation (1) from (2), we get

\((a+6d)-(a+2d)=9-5\)

\(\Rightarrow4d=4\)

\(\Rightarrow d=\frac44=1\)

\(\therefore a=5-2d\)                (From (1))

\(=5-2=3\)

Hence, common difference of given arithmetic progression is d = 1.

Answer 2

Correct option is A) 1