Question

Find
Sum of
the number of terms if
an A.P. 9, 17, 25 is
636?​

Answer 1

Answer:

Answer

Here,

a

1

=9

a

2

=a

1

+d=17

9+d=17

d=8

We know that, the sum of n terms of an A.P. is,

S

n

=

2

n

{2a+(n−1)d}

According to the question,

636=

2

n

{2(9)+(n−1)8}

1272=18n+8n

2

−8n

8n

2

+10n−1272=0

4n

2

+5n−636=0

n=12,−13.25

Ignore the negative value.

n=12

Hence, 12 terms of the A.P. is required to give a sum of 636.

Answer 2

Answer:

n = 12

Step-by-step explanation:

a=9 , d=8 , S=636

Sn=n/2 (2a+(n-1)d)

Substituting values,

636 = n/2 (2(9)+(n-1)8)

636 = n/2 (18+8n-8)

636 = n/2 (10+8n)

636 = n/2×2(5+4n)

636 = n(5+4n)

636 = 5n+4n²

4n²+5n-636

n=12