Prove that a_{m + n} + a_{m - n} =2a_{m}
Ans: a _{m + n} = a_{1} + (m + n - 1) d
a _{m-n} = a_{1} + (m - n -1) d
a_{m} = a_{1} + (m-1) d
Add 1 & 2
a _{m+n} + a_{ m-n }= a_{1}+(m+n-1) d+ a_{1} + (m-n-1)d
= 2a_{1}+(m+n+m-n-1-1)d
= 2a_{1}+ 2(m-1)d
= 2[a_{1}+ (m-1)d]
= 2a_{m}. Hence proved.