If the sum of the first $n$ terms of an AP is $4 n - n^{2}$ , what is the first term (remember the first term is $S_{1}$ )? What is the sum of first two terms? What is the second term? Similarly, find the 3rd , the 10th and the $n$ th terms.

Open in App

Solution

Given that, sum of first n numbers $= 4 n - n^{2}$

$\Rightarrow$ first term $n = 1$

$\Rightarrow 4 (1) - (1)^{2} = 3 \dots (1)$

$\Rightarrow$ sum of first $2$ terms $= 4 (2) - 2^{2}$

$\Rightarrow$ $8 - 4 = 4 \dots (2)$

From (1) and (2)

$\Rightarrow$ $3 + 2^{n d} t e r m = 4$

$\Rightarrow$ $2^{n d} = 1$

$\Rightarrow$ $d = 1 - 3$ $= - 2$

$\Rightarrow$ $A P \to 3, 1, - 1......$

$t_{n} = a + (n - 1) d$

$10^{t h} t e r m \Rightarrow a + 9 d$

$\Rightarrow 3 + 9 (- 2)$

$\Rightarrow 3 - 18 = - 15$

$\Rightarrow$ $n^{t h}$ term $\Rightarrow a + (n - 1) d$

$\Rightarrow 3 + (n - 1) (- 2)$

$\Rightarrow 3 - 2 n + 2$

$\Rightarrow n^{t h} = 5 - 2 n$

Suggest Corrections

Similar questions

If the sum of the first n terms of an AP is (4n− $n^{2}$ ), 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 $3^{r d}$ , the $10^{t h}$ and the $n^{t h}$ terms.

Q. Question 11
If the sum of the first n terms of an AP is

4 n - n^{2}

, what is the first term

(t h a t i s S_{1})

? What is the sum of first two terms? What is the second term? Similarly find the

3^{r d}

, the

10^{t h}

and the

n^{t h}

terms.

If the sum of the first n terms of an AP is 4n-n2 what is the first term that is S1 ? What is the sum of first two terms? What is the second term similarly find the third and 10th and nth terms

Q. If the sum of the first n terms of an