Question

The sum of the first seven terms of an a.p is 182 . if it's 4th and the 17th terms are in the ratio 1:5 , find the a.p.

Answer 1

Answer:

Given,

S

7

=

2

7

[2a+(7−1)d]=182

182=

2

7

[2a+6d]........(1)

a

n

=a+(n−1)d

a

4

=a+(4−1)d=a+3d

a

17

=a+(17−1)d=a+16d

From given, we have,

a

17

a

4

=

a+16d

a+3d

5

1

=

a+16d

a+3d

5a+15d=a+16d

solving the above equation, we get,

4a=d

using this value in (1), we get,

182=

2

7

[2a+6(4a)]

solving the above equation, we get,

a=2

4(2)=8=d

The series as follows,

a,a+d,a+2d,.........

⇒2,10,18,.......

Step-by-step explanation:

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