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