vi) given a=2, d=8, S = 90, find n and an
Answers
Answer:
a=2,d=8,s
n
=90
s
n
=
2
n
[2a+(n−1)d]
90=
2
n
[4+(n−1)8]
180=n[8n−4]
180=8n
2
−4n
=8n
2
−4n−180=0
=2n
2
−n−45=0
=2n
2
−10n+9n−45=0
=2n(n−5)−9(n−5)
=(2n−9)(n−5)
n=5
a
n
=a+(n−1)d
a
n
=2+(5−1)8
a
n
=2+32
a
n
=34
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hunk537
hunk537
03.03.2017
Math
Secondary School
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Answered
In an Ap given , a=2 , d=8 , sn = 90 . find n and an
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Sn = 90
Sn = n/2 [ 2a + (n - 1)d]
90 = n/2 [ 2 x 2 + (n - 1)8]
180/n = 4 + 8n - 8
180/n = 8n - 4
180 = 8n^2 - 4n
8n^2 - 4n - 180 = 0
2n^2 - n - 45 = 0
2n^2 - 10n + 9n - 45 = 0
2n( n - 5) + 9( n - 5) = 0
(2n + 9)(n - 5) = 0
n = -9/2 or n = 5
But n cannot be negative.
So, n = 5
an = a + (n - 1)d
a5 = 2 + (5-1)8
a5 = 2 + 4 x 8
a5 = 2 + 32 = 34