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The sum of first n terms of A.P. is 5n-2n^{2}. Find the A.P. i

Question

The sum of first $n$ terms of $A . P .$ is $5 n - 2 n^{2}$ . Find the $A . P .$ i.e., $a$ and $d$ .

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The sum of first

n

terms of

A . P .

5 n - 2 n^{2}

. Find the

A . P .

i.e.,

a

and

d

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Given that the sum of first n terms an A.P is

5 n - 2 n^{2}

S_{n} = 5 n - 2 n^{2}

First term,

a_{1} = S_{1} = 5 (1) - 2 (1)^{2} = 3

Sum of first two terms ,

S_{2} = 5 (2) - 2 (2)^{2} = 2

Second term ,

a_{2} = S_{2} - S_{1} = 2 - 3 = - 1

Common difference

d = a_{2} - a_{1} = - 1 - 3 = - 4

a_{n} = a + (n - 1) d

a_{n} = 3 + (n - 1) (- 4)

a_{n} = 3 - 4 n + 4

a_{n} = 7 - 4 n

n t h

term of an A.P

= 7 - 4 n

Therefore A.P is

3, - 1, - 5, - 9........

∴ a = 3, d = - 4

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Question Text	The sum of first $n$ terms of $A . P .$ is $5 n - 2 n^{2}$ . Find the $A . P .$ i.e., $a$ and $d$ .
Answer Type	Text solution:1
Upvotes	150