Question

In an A.P. a=2 , d=8 if sum of n terms is 90. Then value of n will be.

Answer 1

Hey friend ☺

Here is your answer

a=2, d=8 and S(n)=90

WE KNOW THAT

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

90=n/2(2×2+(n-1)8)

90×2=n(4+8n-8)

180=n(8n-4)

180=8n²-4n

8n²-4n-180=0

4(2n²-n-45)=0

2n²-n-45=0

2n²-10n+9n-45=0

2n(n-5)+9(n-5)=0

(2n+9)(n-5)=0

2n+9=0

n=-9/2(rejected)

n-5=0

n=5

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HOPE THIS HELPS YOU ☺

Answer 2

Hii friend◆◆◆◆◆◆◆◆◆
your ans is given below...........
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■Given that a=2, d=8 , and s(n)=90


we know that,

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

=》90=n/2 [2×2+(n-1)8]

=》90×2=n(4+8n-8)

=》180=n (8n-4)

=》180=8n^2-4n

=》8n^2-4n-180=0

=》4 (2n^2-n-45)=0

=》2n^2-n-45=0

=》2n^2-10n+9n-45=0

=》2n (n-5)+9 (n-5)=0

=》(2n+9)(n-5)=0

so,2n+9=0, n-5=0

n=-9/2 or n=5

-9/2 is impossible or rejected

so the value of n is 5

....♥♥♥thank you♥♥♥..........

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