# Arithmetic Progressions

#### Question 11:

If the sum of the first
*n* terms of an AP is 4*n* − *n*^{2},
what is the first term (that is *S*_{1})? What is the
sum of first two terms? What is the second term? Similarly find the
3^{rd}, the10^{th} and the *n*^{th}
terms.

#### Answer:

Given that,

*S*_{n}
= 4*n* − *n*^{2}

First term, *a* =
*S*_{1} = 4(1) − (1)^{2} = 4 − 1 = 3

Sum of first two terms
= *S*_{2}

= 4(2) − (2)^{2}
= 8 − 4 = 4

Second term, *a*_{2}
= *S*_{2} − *S*_{1} = 4 − 3 = 1

*d* = *a*_{2}
−...

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