Question

The second term of an H.P. is 314   and fifth term is 110 .  Find the sum of its 6th and 7th term then prove that
513/3233​

Answer 1

Answer:

We have,

Let first term is an A.P.

a=−14

Fifth term is a

5

=a+4d=2

Put a=−14 and we get,

a+4d=2

−14+4d=2

4d=2+14

4d=16

d=4

Find the value of n

Whose sum is 40.

Then,

We know that,

S

n

=

2

n

(2a+(n−1)d)

⇒40=

2

n

(2×(−14)+(n−1)×4)

⇒80=n(−28+4n−4)

⇒80=n(−32+4n)

⇒4n(n−8)=80

⇒n(n−8)=20

⇒n

2

−8n−20=0

⇒n

2

−(10−2)n−20=0

⇒n

2

−10n+2n−20=0

⇒n(n−10)+2(n−10)=0

⇒(n−10)(n+2)=0

For

n+2=0

n=−2

It is not possible (negative)

For,

n−10=0

n=10

Hence, this is the answer.