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You have a geometric sequence where each term $a_m$ is given by $a_m = 7 \times 3^{m-1}$, for $m$ in the set of positive integers. Calculate the total of the first five terms of this sequence.
595
503
579
Consider an arithmetic sequence defined by $t_n = 3n - 2$, where $n$ is a positive integer.
(a)
(i) Use sigma notation to write an expression for the sum $t_1 + t_2 + t_3 + \cdots + t_{15}$.
(ii) Calculate the total of the sum from part (a)(i).
Consider a geometric sequence defined by $w_n = 5 \times 3^{n-1}$, where $n$ is a positive integer.
(b) Find the sum of the first 6 terms of the geometric series $\sum_{m=1}^{6} w_m$.
561
512
592
Consider these geometric series and calculate their sums:
a. $$\sum_{j=1}^{15} 5 \cdot 3^{j-1}$$
b. $$\sum_{m=1}^{20} \left(\frac{3}{4}\right)^{m-2}$$
556
514
532
