In an A.P.:
given a=2,d=8,Sn=90, find n and an
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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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