Question

The sum of the first nth term of series is given by Sn = n^2+5n-6. Find the general term(tn) and(t20).​

Answer 1

EXPLANATION.

Sum of Nth term → Sn = n² + 5n - 6.

→ Tn = Sn - S(n-1).

→ n² + 5n - 6 - [ ( n - 1)² + 5( n - 1) - 6 ].

→ n² + 5n - 6 - [ ( n² + 1 - 2n ) + 5n - 5 - 6 ].

→ n² + 5n - 6 - [ n² + 1 - 2n + 5n - 11 ].

→ n² + 5n - 6 - n² - 1 + 2n - 5n + 11.

→ 2n + 4 = Algebraic expression.

→ n = 1 → 2(1) + 4 = 6.

→ n = 2 → 2(2) + 4 = 8.

→ n = 3 → 2(3) + 4 = 10.

→ n = 4 → 2(4) + 4 = 12.

Series are = 6,8,10,12,.........

First term = a = 6.

Common difference = d = b - a = 8 - 6 = 2.

Nth term Formula.

Tn = a + ( n - 1)d.

Tn = 6 + ( n - 1)2.

Tn = 6 + 2n - 2.

Tn = 2n + 4.

20th term of an Ap.

→ a + 19d.

→ 6 + 19(2).

→ 44.

Tn = 2n + 4 and 20th term = 44.