Question

if the 10th term of an ap is 21 and the sum of its first 10 terms is 120 find its n term​

Answer 1

Answer:       Its nth term is 2n + 1

Step-by-step explanation:

Given :  

a10 = 21 , S10 = 120

Let 'a' be the first term and 'd' be the common difference of the given AP.

Case 1 :  

a10 = 21

By using the formula ,an = a + (n - 1)d

a + (10 - 1) d = 21

a + 9d = 21  

a = 21 - 9d …………….(1)

Case 2 :

S10 = 120

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

S10 = 10/2[2a + (10 - 1)d]

120 = 5 [2a + 9d]

120/5 = 2a + 9d

24 = 2a + 9d

24 = 2 (21 – 9d) + 9d  

[From eq (1)]

24 = 42 - 18d + 9d

24 - 42 = - 9d

-18 = -9d

18 = 9d

d = 18/9

d = 2

On putting the value of d in eq (1),

a = 21 - 9d

a = 21 – 9(2)

a = 21 - 18

a = 3

By using the formula nth term ,an = a + (n - 1)d

an =  3 + (n – 1) 2

an = 3n + 2n – 2

an = 2n + 1

Hence, its nth term is 2n + 1

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Answer 2

Answer:

if the 10th term of an ap is 21 and the sum of its first 10 terms is 120 find its n term 2n+1