Question

The nth term of an AP whose first term is 'a' and common difference is 'd' is a+(n-1)d.proof that mathematical induction

Answer 1

We have to prove that,

$\large T_n=a+(n-1)d$

by Principle of Mathematical Induction.

Let  $n=1.$

$T_1=a+(1-1)d\\ \\ T_1=a+0\times d\\ \\ T_1=a$

Yes, it's correct!

Let  $n=k.$

Assume that  $T_k=a+(k-1)d.$

Let  $n=k+1.$

$T_{k+1}=a+(k+1-1)d\\ \\ T_{k+1}=a+(k-1+1)d\\ \\ T_{k+1}=a+(k-1)d+d\\ \\ T_{k+1}=T_{k}+d$

$\huge \textsc{\underline{\underline{Hence Proved!!!}}}$

Answer 2

Answer:

Ans :; a+(n-1)d..

an= a+(n-1)d