Consider a Geometric progression 1,7,49...7^364 . find the remainder when sum of this g.p is divided by 5.?

1 Answer
Dec 13, 2017

1

Explanation:

In this GP,

a = 1, r = 7, N = 365

S_N = a1*(r^N-1)/(r-1)

S_N = 1*(7^365-1)/(7-1)

S_N = (7^365-1)/6

Sum of digits of 7^365 is 7, so 7^365-1 is divisible by 6.
Last digit of 7^365 is 7.
when divided by 5, 7^365 would leave a remainder 2 ,subract 1, the remainder would be 1