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A sequence starts with 4 and increases in such a way that the second term is 8 and the third term is 12.
(a) Determine the constant increment, $c$, for the sequence.
(b) Calculate the following:
(i) The 15th term of the sequence, $t_{15}$;
(ii) The sum of the first 15 terms, $S_{15}$.
(c) If the term $t_m = 364$, find the value of $m$.
546
585
593
The first term of an infinite geometric sequence is 24, while the fourth term is 3.
(a) Determine the common ratio.
(b) Calculate the sum of the sequence
(c) List the first three terms of sequence.
564
552
526
The first three terms of an arithmetic sequence are $u_1$, $5u_1 - 8$, and $3u_1 + 8$.
(a) Show that $u_1 = 4$.
(b) Prove that the sum of the first $n$ terms of this arithmetic sequence is a square number.
501
520
524
Consider the geometric sequence 32, 16, $x$, 4, $y$, ...
(a) Determine the common ratio.
(b) Find the value of (i) $x$; (ii) $y$.
(c) Calculate $S_9$.
514
536
597
The sum of an infinite geometric series is 18. The second term of the series is 4. Find the possible values of the common ratio $r$.
565
559
574
Calculate the sum of the following infinite geometric series:
(a) 30 + 15 + 7.5 + 3.75 + ...
(b) 10 - 5 + 2.5 - 1.25 + ...
587
510
573
