Question

How many terms of the AP:9,17,25……must be taken to give a sum of 636?

Answer 1

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Answer 2

Answer:

n=12 (no. of terms =12)

Step-by-step explanation:

To find no. of terms we should use this formula:

S=n/2[2a+(n-1)d]

then on substituting a=9 ; d=17-9=8 ; S=636. we get

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

=636 x 2=n[18+8n-8]

=1272=n[10+8n]

=1272=10n+8n^2

=8n^2+10n-1272=0 (on solving this quadratic equation)

=2(4n^2+5n-636)=0

=4n^2-48n+53n-636=0

=4n(n-12)+53(n-12)=0

=(n-12) (4n+53)=0

=n= -53/4 ; n=12.

n should not be with a negative sign therefore, the answer is 12.