Question

if the sum of first n terms of an ap is given by sn=(3n2+2n), find its 25th term​

Answer 1

Answer:

hi_______friend__

Step-by-step explanation:

Given, sum of first n terms of an AP, Sn = 3n2 – n

Sn = 3n2 – n

Replacing n by n – 1, we get

Now,put n = 1 in an, we get a = 6×1−4 = 2put n = 2 in an, we get a2 = 6×2−4 = 8put n = 3 in an, we get a3 = 6×3−4 = 14and so on.So, required AP is, 2,8,14,.....

Putting n = 25, we get

a25 = 6 × 25 – 4 = 150 – 4 = 146

Thus, the 25th term of given ap is 146

Answer 2

Answer:

149

Step-by-step explanation:

we know that,

sₙ = ( 3n^2 + 2n )

so,

s₁ = [ 3(1)^2 + 2(1)] = 3 + 2 = 5

s₂ = [ 3(2)^2 + 2(2) ]

= [ 3(4) + 4 ]

= 12 + 4

= 16

We also know that S₁ = a₁ and S₂ = a₁ + a₂

therefore,

a₁ = 5

a₂ = s₂ - a₁ = 16 - 5 = 11,

d = 11 - 5 = 6,

aₙ = a + ( n - 1 ) d,

a₂₅ = 5 + 24(6)

= 5 + 144

= 149

therefore the 25th term is 149