Multiple choice

If the difference between the nth term and (n - 1)th term of a sequence is 2n - 4 for all n ≥ 2. and the first term of sequence is -2, then the 100th term of the sequence is

  1. 7,090

  2. 9,070

  3. 9,700

  4. 7,900
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

T(n) - T(n-1) = 2n - 4. T(n) = T(1) + sum_{k=2 to n} (2k - 4). T(1) = -2. Sum = 2 * sum(k) - sum(4) = 2 * (n(n+1)/2 - 1) - 4(n-1) = n^2 + n - 2 - 4n + 4 = n^2 - 3n + 2. T(n) = -2 + n^2 - 3n + 2 = n^2 - 3n. For n=100, T(100) = 10000 - 300 = 9700.

Keep practicing — related questions