No questions found
In an arithmetic sequence, the fifth term $u_5$ is equal to the sum of the first five terms $S_5$. If $u_5$ is 15, what are the first term $u_1$ and the common difference $d$?
100
21
576
(a) Consider the sequence $1, 8, 27, 64, 125, \dots$. Derive a formula for the general term $S_k$ of the sequence.
(b) Compute $S_k$ for $k = 1, 2, 3, 4,$ and $5$.
3000
143
525
The 20th term of an arithmetic sequence is 75 and the common difference, $d$, is 3.5.
Find $S_{20}$, the sum of the first 20 terms of the arithmetic sequence.
3000
123
519
The sum of the first $n$ terms of an arithmetic sequence is given by $S_n = pn^2 - qn$, where $p$ and $q$ are positive constants. It is given that $S_5 = 65$ and $S_6 = 96$.
(a) Find the value of $p$ and the value of $q$.
(b) Find the value of $u_6$.
510
546
510
The seventh term, $b_7$, of an arithmetic sequence is 30. The fifteenth term, $b_{15}$, of the same sequence is 62.
(a) Determine $e$, the common difference of the sequence.
(b) Calculate $b_1$, the first term of the sequence.
545
579
514
