Question

If N = 14 + 24 + 34 +................+ 784 . Find the remainder,when N is divided by 5

Answer 1

start by cointing number of terms

Answer 2

*counting

Answer 3

nth term of an arithmetic series is: a + (n-1)d
a = 14, d = 10, last term = 784. find n.

Answer 4

n=2/5

Answer 5

\(N=(4+\dots+4)+10\cdot(1+\dots+78)=4\cdot78+10\cdot(1+\dots+78)\)

Answer 6

so \(N\equiv4\cdot78\equiv4\cdot8\equiv32\equiv2\pmod5\)

Answer 7

note \(4\cdot78\equiv4\cdot(70+8)\equiv4\cdot8\pmod{5}\) is the logic I used to jump from \(78\) to \(8\) there, sorry if that wasn't clear

Answer 8

understood @oldrin.bataku ,thanks to @ganeshie8 ,@ranga

Answer 9

np