Question

An Arithmetic Progression of positive integers has its $n^{th}$ term as ${66541}^{8768}$. Find the first term of this Arithmetic Progression if the common difference = 9.

• A. 1
• B. 2
• C. 7

Answer 1

The correct option is C 7

From constant remainder theorem, if any of the terms in an AP is divided by the common difference, the remainder will be constant in each case.

Let us find the remainder when the $n^{th}$ term of the AP is divided by 9

$rem\frac{{66541}^{8768}}{9}=rem\frac{4^{8768}}{9}rem$

The number changes to $\frac{4^2}{9}=\frac{16}{9}$ (Rem) = 7.