Question

If sum of n terms of an AP is 3n2- 2n, find nth term and 10th term.Also find difference of an A.P.​

Answer 1

Answer:

aₙ = 6n - 5

a₁₀ = 55

d = 6

Step-by-step explanation:

Given----> Sₙ = 3n² - 2n

To find -----> nth term and 10th term of AP and common difference of AP .

Solution-----> ATQ,

Sₙ = 3n² - 2n

Putting n = 1 , in it we get,

=> S₁ = 3 ( 1 )² - 2 ( 1 )

=> S₁ = 3 ( 1 ) - 2

=> S₁ = 3 - 2

=> S₁ = 1

S₁ means sum of only one term , it means ,

a = S₁

=> a = 1

Now putting n = 2 in Sₙ , we get,

S₂ = 3 ( 2 )² - 2 ( 2 )

= 3 ( 4 ) - 4

= 12 - 4

=> S₂ = 8

S₂ , means sum of two terms ,

=> a₁ + a₂ = 8

Putting a₁ = 1 , we get ,

=> 1 + a₂ = 8

=> a₂ = 8 - 1

=> a₂ = 7

Common difference ( d ) = a₂ - a₁

d = 7 - 1

d = 6

Now aₙ = a + ( n - 1 ) d

=> aₙ = 1 + ( n - 1 ) 6

=> aₙ = 1 + 6n - 6

=> aₙ = 6n - 5

Putting n = 10 , we get,

a₁₀ = 6 ( 10 ) - 5

=> a₁₀ = 60 - 5

=> a₁₀ = 55