Question

1. How many terms of the AP: 9.17.25.... must be taken to give a sum of 636?​

Answer 1

Answer:

12

Number of terms of the AP [ 9 , 17 , 25 ] which are required to make the sum of 636 is 12.

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Answer 2

Answer:

n= 12

Step-by-step explanation:

given, a=9 and sn=636

d=17-9

=8

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

636=n/2[2x9+(n-1)8]

636=n/2x2[9+(n-1)4]. (taking out 2)

636=n[9+4n-4]

636=n[5+4n]

636=5n+4n^2

4n^2 +5n -636 =0

solving. the above quadratic equation, we have

= 4n^{2} -48n + 53n - 636

=4n^{2} −48n+53n−636

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

=4n(n−12)+53(n−12)

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

=(4n+53)(n−12)

we have two values of n,

n=12 and n= -53/4

correct ans is, n= 12