Question

For what value of n, terms of two AP 63,65,67,....and 3,10,7,....equal?

Answer 1

Let the 1st AP be A =63,65,68.....

Let the 2nd AP be B = 3,7,17......

For A , common difference is : 65-63 = 2

For B ,common difference is : 10-3 = 7

Now Let the nth term be An and Bn respectively.

According to question

An = Bn

=> 63+(n-1)2 = 3+(n-1)7

=>60 + 2n-2 = 7n-7

=>65 = 5n

=> n = 13

Thus 13th term of both AP's will be same

Hope It helps you

Answer 2

first case,

A•P=63,65,67.......

a=63

d=65--63=2

n=?

an=?

an=a+(n--1)d

=63+(n--1)2

=2n+61........ (1)

second case,

A•P=3,10,17.......

a=3

d=10--3=7

n=?

an=?

an=a+(n-1)d

=3+(n--1)7

=7n--4......... (2)

from eq.(1)&(2),

2n+61=7n--4

61+4=7n--2n

5n=65

n=65/5=13