Question

If the first and fifth term’s sum is 10, then the third term of an arithmetic progression is……………… 

A) 3 

B) 1 

C) 5 

D) 2

Answer 1

Correct option is (C) 5

Given that \(a_1+a_5=10\)

\(\Rightarrow a+(a+4d)=10,\) where d is common difference    \((\because a_n=a+(n-1)d)\)

\(\Rightarrow2a+4d=10\)

\(\Rightarrow a+2d=\frac{10}2=5\)

\(\therefore a_3=5\)           \((\because a_3=a+2d)\)

Hence, third term of given A.P. is 5.

Answer 2

Correct option is C) 5