Question

how many terms of the AP: 9,17,25,...must be taken to give a sum of 636?​

Answer 1

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.

Step-by-step explanation:

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Answer 2

where is the sum of first term to nth term of the AP, a is the first term, d is the common difference and n is the number of terms of AP. In the given Question, sum of APs is 636. Hence, Number of terms of the AP [ 9 , 17 , 25 ] which are required to make the sum of 636 is 12

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