Multiple choice

If the terms of a sequence is defined by Sn = 5 81 − n , n ≥ 1 . For a positive integer m, let Um = Sm + Sm-1 + Sm-2 + ....... + S1, i.e. Um denotes the sum of first m terms of the sequence. Find the value of U51 - U50.

  1. (531 + 530)

  2. (531 + 1)

  3. (530 – 1)

  4. 530

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interpreting the sequence as S_n = 5^(81-n), the difference U_51 - U_50 contains only the 51st term, S_51. Therefore, S_51 = 5^(81-51) = 5^30.

AI explanation

By definition, U51 is the sum of the first 51 terms and U50 is the sum of the first 50 terms. Therefore, U51 minus U50 equals the 51st term, which is S51. Substituting n equal to 51 into the formula gives 5 to the power of 81 minus 51, resulting in 5 to the power of 30. The value is 530.

Keep practicing — related questions