in an ap:
(1)given a=2,d=3,an=50,find n and sn
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We have,

Now,
![\quad \: S_n \\ \\ = \frac{n}{2} \left[ 2a + (n - 1)d \right] \\ \\ = \frac{17}{2} \left[ 2(2) + (17 - 1)(3) \right] \\ \\ = \frac{17}{2} \left[ 4 + 16(3) \right] \\ \\ = \frac{17}{2} (4 + 48) \\ \\ = \frac{17}{2} \times 52 = \frac{17}{ \cancel{2} \: _1} \times \cancel{52} \: {}^{26} \\ \\ = 17 \times 26 \\ \\ = \quad \bf442 \quad \: S_n \\ \\ = \frac{n}{2} \left[ 2a + (n - 1)d \right] \\ \\ = \frac{17}{2} \left[ 2(2) + (17 - 1)(3) \right] \\ \\ = \frac{17}{2} \left[ 4 + 16(3) \right] \\ \\ = \frac{17}{2} (4 + 48) \\ \\ = \frac{17}{2} \times 52 = \frac{17}{ \cancel{2} \: _1} \times \cancel{52} \: {}^{26} \\ \\ = 17 \times 26 \\ \\ = \quad \bf442](https://tex.z-dn.net/?f=+%5Cquad+%5C%3A+S_n+%5C%5C+%5C%5C+%3D+%5Cfrac%7Bn%7D%7B2%7D+%5Cleft%5B+2a+%2B+%28n+-+1%29d+%5Cright%5D+%5C%5C+%5C%5C+%3D+%5Cfrac%7B17%7D%7B2%7D+%5Cleft%5B+2%282%29+%2B+%2817+-+1%29%283%29+%5Cright%5D+%5C%5C+%5C%5C+%3D+%5Cfrac%7B17%7D%7B2%7D+%5Cleft%5B+4+%2B+16%283%29+%5Cright%5D+%5C%5C+%5C%5C+%3D+%5Cfrac%7B17%7D%7B2%7D+%284+%2B+48%29+%5C%5C+%5C%5C+%3D+%5Cfrac%7B17%7D%7B2%7D+%5Ctimes+52+%3D+%5Cfrac%7B17%7D%7B+%5Ccancel%7B2%7D+%5C%3A+_1%7D+%5Ctimes+%5Ccancel%7B52%7D+%5C%3A+%7B%7D%5E%7B26%7D+%5C%5C+%5C%5C+%3D+17+%5Ctimes+26+%5C%5C+%5C%5C+%3D+%5Cquad+%5Cbf442)
Hence,

and,

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Additional Information

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In a sequence, if the difference between two consecutive terms is same then the sequence is known as an A.P.
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The first term is known as " a " .
The common difference is known as " d " .
The 'nth term' is given by :![\Large\sf\red{\underline{\fbox{\green{a_n = [a + (n - 1)d]}}}} \Large\sf\red{\underline{\fbox{\green{a_n = [a + (n - 1)d]}}}}](https://tex.z-dn.net/?f=%5CLarge%5Csf%5Cred%7B%5Cunderline%7B%5Cfbox%7B%5Cgreen%7Ba_n+%3D+%5Ba+%2B+%28n+-+1%29d%5D%7D%7D%7D%7D)
The sum of 'n' terms is given by :![\Large\sf\red{\underline{\fbox{\green{S_n = \frac{n}{2} [2a + (n - 1)d]}}}} \Large\sf\red{\underline{\fbox{\green{S_n = \frac{n}{2} [2a + (n - 1)d]}}}}](https://tex.z-dn.net/?f=%5CLarge%5Csf%5Cred%7B%5Cunderline%7B%5Cfbox%7B%5Cgreen%7BS_n+%3D+%5Cfrac%7Bn%7D%7B2%7D+%5B2a+%2B+%28n+-+1%29d%5D%7D%7D%7D%7D)
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Now,
Hence,
and,
__________________________
Additional Information
_______________________________________
In a sequence, if the difference between two consecutive terms is same then the sequence is known as an A.P.
_______________________________________
The first term is known as " a " .
The common difference is known as " d " .
The 'nth term' is given by :
The sum of 'n' terms is given by :
_______________________________________
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