Question

find n so that the nth term of the following to A.P.s are the same
1,7,13,19,........... . and 100,95,90,...

Answer 1

a= first term= 1

d= common difference= 7-1 and 13-7 is 6

n= no. of terms.

thus , nth term = an

an= a+ (n-1)d

an= 1+ (n-1)6

an = 1-6 +6n

an = 6n-5.

and for the second a.p,

a= 100

d= 95-100 and 90-95 = -5

an = a+ (n-1)d

an = 100 + ( n-1)-5

an= 100+5 -5n

an = 105-5n