Math, asked by sanapbhagwati45, 2 months ago

The second term of the series, the sum of whose n
th term is 2n2 + 5n is:

Answers

Answered by amansharma264
5

EXPLANATION.

Nth term = 2n² + 5n.

As we know that,

⇒ Tₙ = Sₙ - Sₙ₋₁.

Put the value of n = n - 1 in the equation, we get.

⇒ Tₙ = 2n² + 5n - [2(n - 1)² + 5(n - 1)].

⇒ Tₙ = 2n² + 5n - [2(n² + 1 - 2n) + 5n - 5].

⇒ Tₙ = 2n² + 5n - [2n² + 2 - 4n + 5n - 5].

⇒ Tₙ = 2n² + 5n - [2n² + n - 3].

⇒ Tₙ = 2n² + 5n - 2n² - n + 3.

⇒ Tₙ = 5n - n + 3.

⇒ Tₙ = 4n + 3.

Algebraic expression = 4n + 3.

Put the value of n = 1 in the equation, we get.

⇒ 4(1) + 3.

⇒ 4 + 3 = 7.

Put the value of n = 2 in the equation, we get.

⇒ 4(2) + 3.

⇒ 8 + 3 = 11.

Put the value of n = 3 in the equation, we get.

⇒ 4(3) + 3.

⇒ 12 + 3 = 15.

Put the value of n = 4 in the equation, we get.

⇒ 4(4) + 3.

⇒ 16 + 3 = 19.

Series = 7, 11, 15, 19. . . . . .

First term = a = 7.

Common difference = d = b - a = c - b.

Common difference = d = 11 - 7 = 4.

Second term = a + d = 7 + 4 = 11.

                                                                                                                   

MORE INFORMATION.

Supposition of terms in A.P.

(1) = Three terms as : a - d, a, a + d.

(2) = Four terms as : a - 3d, a - d, a + d, a + 3d.

(3) = Five terms as : a - 2d, a - d, a, a + d, a + 2d.

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