Question

answer this question ​

Answer 1

Step-by-step explanation:

1. s=n/2( a+1)
2. 120=10/2( a+21)
3. a=3
4. t= a+( n-1) d
5. 21= 3+(10-1) d
6. d=2
7. nth term = 3+( n-1)2
8. = 3+2 n-2 =2 n +1....

Answer 2

Step-by-step explanation:

Let’s consider a to be the first term and d be the common difference

. And we know that, sum of first n terms is:

Sn = n2n2(2a + (n − 1)d) and nth term is given by: an = a + (n – 1)d

Now, from the question we have

S10 = 120

⟹ 120 = 10/2 ( 2a + (10 − 1)d)

⟹ 120 = 5(2a + 9d)

⟹ 24 = 2a + 9d …. (1)

Also given that, a10 = 21

⟹ 21 = a + (10 – 1)d

⟹ 21 = a + 9d …. (2)

Subtracting (2) from (1), we get

24 – 21 = 2a + 9d – a – 9d

⟹a = 3

Now, on putting a = 3 in equation (2), we get

3 + 9d = 21

9d = 18

d = 2

Thus, we have the first term(a) = 3 and the common difference(d) = 2

Therefore, the nth term is given by

an = a + (n – 1)d = 3 + (n – 1)2

= 3 + 2n -2 = 2n + 1

Hence, the nth term of the A.P is (an) = 2n + 1.