Question

Determine the AP whose 3rd term is 5 and the 7th term is 9.
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Answer 1

3rd term = 5

a+2d = 5.......(1)

7th term = 9

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

(2) - (1)

a+6d=9

-(a+2d=5)

4d=4

d=4/4

d=1

put the value of d in equation (1)

a+2d=5

a+2(1)=5

a+2=5

a=5-2

a=3

a.p. series are:- 3,4,5,6,7,8,9,......

Answer 2

Answer:

$\boxed{\bold{\mathsf{A.P\: is \: 3,4,5,6,7.......}}}$

Step-by-step explanation:

Given Series is in Airthmatic progression

• General term in A.P :-

$\implies{\mathsf{A_n = a + (n -1)d}}$

$\rule{200}{2}$

Given relations :-

$\implies{\mathsf{A_3 = 5 \: and \: A_7 \: = \: 9 }}$

$\implies{\mathsf{A_3 =a+(3-1)d= 5}}$

$\rule{200}{2}$

$\implies{\mathsf{A_3 = a +2d= 5 }}$.....(1)

$\implies{\mathsf{A_7 =a +(7-1)d= 9 }}$

$\implies{\mathsf{ = a +6d = 9}}$....(2)

On solving Equation (1) & (2)

a +2d= 5 $\implies{\mathsf{}}$ a = 5 - 2d

Now put this in (2)

a +6d = 9

5 - 2d +6d = 9

4d = 4

$\implies{\mathsf{d = 1 }}$

Now put " d" value in any of the equation

a + 6(1) = 9

$\implies{\mathsf{a = 3 }}$

$\boxed{\huge{\implies{\bold{\mathsf{A.P\: is \: 3,4,5,6,7.......}}}}}$