Question

In am AP 10th term is 21 and sum of first 10 term is 120 find the n the term of Arethametic progration​

Answer 1

Answer: The nth term $a_{n} =$ 2n + 1

Step-by-step explanation:

Formula(s):

$a_{n}$ = a + (n − 1) × d

S = n/2[a + a + (n − 1) × d]

Given:

1. 10th term = 21

• a + 9d = 21... (i)

2. Sum of first ten terms = 120

10/2 [a + a + (10-1) d] = 120

5 [a + a + 9d] = 120

5 [a + 21] = 120

[a + 21] = 120/5 = 24

a +21 = 24

• a = 3

Now, put a = 3 in the first equation:

a+9d = 21

3 + 9d = 21

9d = 18

• d = 2

Now, general term is:

$a_{n}$ = a + (n − 1) × d

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

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

$a_{n} = 2n + 1$

Answer: The nth term $a_{n} =$ 2n + 1

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