Answer:
\large{\mathcal{QUESTION:}}QUESTION:
1. Find the sum of the first five terms of the geometric sequence (17.-51. 153,..).
a. 1073
b. 1037
C. 1 299
d. 1 999
\begin{gathered} \\ \end{gathered}
\large{\mathcal{SOLUTION:}}SOLUTION:
Given: A_1 = 17
\rm{r = A_2÷A_1}r=A2÷A1
\rm{r = -51÷17}r=−51÷17
\rm{r = -3}r=−3
Solving using the sum of finite geometric sequence formula:
\rm{S_n =A_1 \frac{1-r^n}{1-r}}Sn=A11−r1−rn
\rm{S_5 =17\bigg(\frac{1-(-3)^5}{1-(-3)}\bigg)}S5=17(1−(−3)1−(−3)5)
\rm{S_5 =17 \bigg(\frac{1-(-243)}{1+3}\bigg)}S5=17(1+31−(−243))
\rm{S_5 =17\bigg(\frac{1+243}{4}\bigg)}S5=17(41+243)
\rm{S_5 =17\bigg(\frac{244}{4}\bigg)}S5=17(4244)
\rm{S_5 =17(61)}S5=17(61)
\boxed{\rm{S_5=1037}}S5=1037
\begin{gathered} \\ \end{gathered}
\large{\mathcal{ANSWER:}}ANSWER:
LETTER B (1037)
