Question

When an integer is divided by 3, the remainder is 1, and when k+ 1 divides by 5, the remainder is 0, what will be the value of k?​

Answer 1

Answer:

Let the no. divided by 3 be x.

Thus

Dividend = divisor×quotient + remainder

x = 3(quotient) + 1

Now for k+1 and 5

k+1 = 5(quotient) + 0

k+1 = 5×quotient

Thus the value of k is

k = 5× quotient -1

Now replacing quotient as 1

k=4

quotient = 2

k=9

quotient = 3

k= 14

Thus the answers form an AP with

a=4

d=5

Thus any one terms of the AP will satify the value of k

thus nth term of AP

= a+ (n-1)d

Thus k = 4+ (n-1)5

where n is the term number

hope this helps!