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Question 45. If sum of the first n terms of an A.P. is 4n – n2, then what is the first term? What is the sum of first two terms? What is the second term? Similarly find the 3rd, 10th and nth terms.

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This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have been given that the  sum of the first n terms of an A.P. is 4n – n2,

We have to. Find out what is the first term.

Also we have to find  the sum of first two terms the second term and Similarly find the 3rd, 10th and nth terms.

CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 45

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1. Given Sn = 4n – n2,

On putting n = 1, we get the first term(a), S1 = a = 4(1) – 12 = 3.

On putting n = 2 gives S2 = a + a + d = 4(2) – 22 = 4

=> d = 4 – 2a

=> d = 4 – 6 = –2

Second term(a2) = a + d = 3 + (–2) = 1

By using the formula of nth term of an A.P.

an = a + (n – 1)d

So,

= 3 + (n – 1)(–2)

= 5 – 2n

Hence, third term(a3) = 5 – 2(3) = –1

And tenth term(a10) = 5 – 2(10) = –15

Hence, the first term is 3, sum of first two terms is 4, second term is 1

and 3rd, 10th and nth terms are –1, –15 and 5 – 2n respectively.

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