Question

if the sum of 1st n terms of an AP is 4n-n2 wat is the 10th term and the nth term

Answer 1

I hope this may help u

Answer 2

Answer:

10th term $a_{10}=-15$

nth term $a_{n}=5-2n$

Step-by-step explanation:

Given : If the sum of 1st n terms of an AP is $4n-n^2$

To find : What is the 10th term and the nth term ?

Solution :

The sum of 1st n terms of an AP is $S_n=4n-n^2$

The first term is at n=1,

$S_n=4n-n^2$

$S_1=4(1)-(1)^2$

$S_1=4-1$

$a_1=3$

The sum of first two term is

$S_2=4(2)-(2)^2$

$a_1+a_2=8-4$

$3+a_2=4$

$a_2=4-3$

$a_2=1$

The first term is 3 , the second term is 1

The common difference is $d=a_2-a_1$

$d=1-3$

$d=-2$

The 10th term of the A.P is

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

$a_{10}=3+(10-1)(-2)$

$a_{10}=3+(9)(-2)$

$a_{10}=3-18$

$a_{10}=-15$

The nth term of the A.P is

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

$a_{n}=3+(n-1)(-2)$

$a_{n}=3-2n+2$

$a_{n}=5-2n$