Multiple choice

Find the sum of 18th and 32nd term of the given sequence. 15, 25, 38, 54, ...

  1. 1019

  2. 1910

  3. 2119

  4. 2313
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sequence: 15, 25, 38, 54. Differences: 10, 13, 16. This is a quadratic sequence. Second difference is 3. General term T(n) = an^2 + bn + c. 2a = 3 => a = 1.5. 3a + b = 10 => 4.5 + b = 10 => b = 5.5. a + b + c = 15 => 1.5 + 5.5 + c = 15 => c = 8. T(n) = 1.5n^2 + 5.5n + 8. T(18) = 1.5(324) + 5.5(18) + 8 = 486 + 99 + 8 = 593. T(32) = 1.5(1024) + 5.5(32) + 8 = 1536 + 176 + 8 = 1720. Sum = 593 + 1720 = 2313.

AI explanation

The differences between consecutive terms are 10, 13, and 16, forming an arithmetic progression with a common difference of 3. Using the formula for the nth term of a sequence, Tn = a + (n - 1)d + ((n - 1)(n - 2)/2)c, we find the 18th term is 15 + 17(10) + (17 * 16 / 2)(3) = 596 and the 32nd term is 15 + 31(10) + (31 * 30 / 2)(3) = 1717. Adding these two terms gives 596 + 1717 = 2313.

Keep practicing — related questions