Question

Sum of n terms of an arithmetic progression is 5n^2-2n, then 18 th term of the series is:​

Answer 1

Answer:

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Answer 2

Given

S

n

=5n

2

+2n ___________ (1)

then S

n−1

=5(n−1)

2

+2(n−1)

S

n−1

=5n

2

+5−10n+2n−2

S

n−1

=5n

2

−8n+3 _________ (2)

We know S

n

−S

n−1

=a

n

then a

n

=5n

2

+2n−5n

2

+8n−3=10n−3 _________ (3)

and a

n

=a

n−1

=d

10n−3−10n+10+3=d

[d=10]

∴ common difference of AP is 10.

a

n

=a+(n−1)10⇒10n−3=a+10n−10

[a=7]

now 18

th

term of AP having a=7 & d=10

a

18

=7+17d=7+170=177

∴18

th

term is 177.