Question

Find the sum of firstn term of the -2,1,4,7.......

Answer 1

ANSWER:-

Sn=n²-3n

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EXPLANATION:-

Here in the given A.P. we can see that first term and common difference of the A.P. can be easily find and we have to find the sum of A.P. upto nth terms. We have to do only is to put value of first term and common difference in the formula to find sum upto nth terms.

So let's start!

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GIVEN A.P.:-

-2,1,4,7...

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First term, a=-2

Common difference, d= a2-a1

=> 1-(-2)

=> 1+2

=> 3

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We have formula for sum upto nth terms:

${\large{\underline{\boxed{\sf{Sn=\dfrac{n}{2}[2a+(n-1)d]}}}}\star}$

$\sf{:\implies Sn=\dfrac{n}{2}[2(-2)+(n-1)2]}$

$\sf{:\implies Sn=\dfrac{n}{2}[-4+2n-2]}$

$\sf{:\implies Sn=\dfrac{n}{2}[-6+2n]}$

$\sf{:\implies Sn=\dfrac{n}{2}[2(-3+n)]}$

$\sf{:\implies Sn=\dfrac{n}{2}[2(-3+n)]}$

$\sf{:\implies Sn=n(-3+n)}$

$\sf{:\implies Sn=-3n+n^{2}}$

$\large{\underline{\boxed{\sf{:\implies Sn=n^{2}-3n}}}}$

∴ The sum of A.P. upto nth term is n²-3n.

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