Question

Find the sum of the first 10 terms in the series 1 × 2, 2 × 3, 3 × 4, .... :

• A. 340
• B. 430
• C. 440
• D. 540

Answer 1

Answer:

C. 440

n th term of the sequence= n(n + 1) Sum of first 10 terms of the sequence = 1 × 2 + ( 2 × 3) + ( 3 × 4 ) + .....+ (10×11) = 1 × (1 + 1) + 2(2+1) + 3(3+1) + ........ + 10(10 + 1) = 1² + 1 + 2² + 2 + 3² + 3 + 4² + 4 + ....... + 10² + 10 = 1² + 2² + 3² + ...... + 10² + 1 + 2 + 3 + ...... + 10 = Sum of squares of the first n numbers + sum of the first n numbers = n(n+ 1)(2n+ 1)/6 + n(n+1)/2 = 10 × 11 × 21/6 + 10 × 11/2 = 385 + 55 = 440