Question

For what value of n, the nth term of the two APs: 3, 8, 13, …. and 19, 22, 25, ….will be equal​

Answer 1

Step-by-step explanation:

nth term of an Ap: n= a+(n-1)d

where, a= 1st term and d= common difference between each term

here, in first Ap: a= 3, d= 8-3= 5

nth term is denoted by tn

so, for first AP, tn= 3+(n-1)5

now in second Ap: a= 19,d= 22-19= 3

so, nth term of second Ap: 19+(n-1)3

both nth terms are equal. so, we should equal both terms.

so, 3+(n-1)5= 19+(n-1)3

3+5n-5= 19+3n-3

so, 5n-2= 3n+16

by taking n terms to LHS side and constants to RHS side...

5n-3n= 16+2

2n= 18

so, n= 18/2=9

n=9

so, for n=9 the 9th term of two APs are equal.....