Question

if the third term of an A.p. is 5 and the seventh term is 9 find the 17th number​

Answer 1

Here,

Third term (a) = 5

Seventh term (b) = 9

17th number = ?

Now,

T3 = a + 2d

5 = a + 2d

d = (5 - a)/2 ------ 1.

T7 = a + 6d

9 = a + 6d

d = (9 - a)/6 ------- 2.

Combining eq (1) and (2)

or, (5 - a)/2 = (9 - a)/6

or, 6 (5 - a) = 2 (9 -a)

or, 30 - 6a = 18 - 2a

or, 12 = 4a

◆ a = 3

putting the value of a in eq (1)

or, d = (5 - 3)/2

or, d = 2/2

◆ d = 1

Then,

T17 = a + 16d

= 3 + 16

= 19

◆ T17 = 19

I hope you understand...

This is Right answer...

Thanks♥♥♥♥