Question

the sum fo 4th and 8th term =22and the product of 2nd and 6th term =33.Find AP?​

Answer 1

Given,

☛ sum of 4th term and 8th term = 22

==> a + 3d + a + 7d = 22

==> 2a + 10d = 22

==> a + 5d = 11 ...(1), also, It is the 6th term)

Also,

☛ product of 2nd term and 6th term = 33

==> ( a + 5d ) * (a + d) = 33

==> 11(a + d) = 33

==> a + d = 3

==> d = 3 - a ...(2)

Putting d = 3 - a in (1)

==> a + 5(3 - a) = 11

==> a + 15 - 5a = 11

==> -4a = -4

==> a = 1 ...(3)

Putting a = 1 in (2)

==> d = 3 - a

==> d = 3 - 1

==> d = 2 ...(4)

A.P = a , a + d, a + 2d, a + 3d, ...

A.P = 1 , 3, 5, 7, 9, ...

Answer 2

As we know that,

4th term = first term +3rd term

similarly,

8th term = first term + 7th term

Therefore,

(first term+3rd term)+(first term+7th term) = 2first term+10th term

= 2(first term+5th term)

= 2×6th term

=226th term

= 22/2

=11

6th term × 2nd term = 33

11×2nd term = 33

2nd term = 33/11= 3

6th term= first term+5th term

2nd term= first term+First term

11-3= (first term+5th term)-(first term+first term)

8= 4th term

1 term = 8/4=2

ap= 1,3,5,7,9,11,13,15,17,..............

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