Question

Determine the AP whose third term is 5 and the seventh term is 9

Answer 1

so here is your answer

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Here,

Given,

3rd term = 5

Also,

7th term = 9

Situation,

a5 = 5

a + 4d = 5 .......... (1)

Also,

a7 = 9

a + 6d = 9 ............ (2)

Now,

Subtract (1) from (2) we get,

a + 6d - a + 4d = 9 - 5

a + 6d - a + 4d = 4

2d = 4

d = 4/2

d = 2

Now,

Substitute the value of d in (1) :-

a + 4d = 5

a + 4 × 2 = 5

a + 8 = 5

a = 5 - 8

a = -3

Hence,

Arithmetic Progression are -3, -1 , 1.........