EXPLANATION.

Sum of first terms of an A.P.

⇒ Sₙ = 2n² + 8n.

As we know that,

⇒ Tₙ = Sₙ - Sₙ₋₁.

⇒ 2n² + 8n - [2(N - 1)² + 8(n - 1)].

⇒ 2n² + 8n - [2(n² + 1 - 2n) + 8n - 8].

⇒ 2n² + 8n - [2n² + 2 - 4n + 8n - 8].

⇒ 2n² + 8n - [2n² + 4n - 6].

⇒ 2n² + 8n - 2n² - 4n + 6.

⇒ 8n - 4n + 6.

⇒ 4n + 6. = Algebraic expression.

As we know that,

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

⇒ 4(1) + 6.

⇒ 4 + 6.

⇒ 10.

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

⇒ 4(2) +  6.

⇒ 8 + 6.

⇒ 14.

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

⇒ 4(3) + 6.

⇒ 12 + 6.

⇒ 18.

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

⇒ 4(4) + 6.

⇒ 16 + 6.

⇒ 22.

Their Series = 10, 14, 18, 22,,,,,,,

First term of an A.P. = a = 10.

Common difference = d = B - a = 14 - 10 = 4.

As we know that,

General terms of an A.P.

⇒ Tₙ = a + (n - 1)d.

⇒ T₁₆ = a + (16 - 1)d.

⇒ T₁₆ = a + 15d.

⇒ T₁₆ = 10 + 15(4).

⇒ T₁₆ = 10 + 60.

⇒ T₁₆ = 70.

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.