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If a(n)=3-4n, then show that a(1),a(2),a...

If `a_(n)=3-4n`, then show that `a_(1),a_(2),a_(3), …` form an AP. Also, find `S_(20)`.

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`a_(n)=3-4n`
`rArr a_(n-1)=3-4(n-1)`
`=3-4n+4=7-4n`
`:. a_(n)-a_(n-1)=(3-4n)-(7-4n)=-4`
Which does not depend on 'n' i.e., the difference of two consecutive terms is constant.
`:.` Given sequence is in A.P.
Now, `a_(1)=a=3-4(1)=-1`,
d=-4
`:. S_(20)=(20)/(2)[2a+(20-1)d]`
`=10[2(-1)+19(-4)]=-780`
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