Question

5,11,17......
Find if 301 is a term?

Answer 1

हलो मित्र,

The terms in the AP are 5+0*6, 5+1*6, 5+2*6, 5+3*6, etc. If 301 is a term, it must be of the form 5+n*6. Set this equal to 301 and solve for n. n needs to be a whole number.

5+n*6 = 301

n*6 = 296

n = 296/6.

296 must be divisible by 6, so it must be divisible by both 2 and 3, the factors of 6.

296 is even so it is divisible by 2. However, the digits in 296 add to a number that is not divisible by 3 (2 + 9 +6 = 17, which is prime and not divisible by 3, so 296 is not divisible by 3.)

Since n is not a whole number, 301 is not a term in the AP.