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Find the sum of an 8-term geometric sequence when the first term is 7 and the last term is 114,688 and select the correct answer below. 152,915 16,384 16,377 152,908

Respuesta :

naǫ
[tex]a_1=7 \\ a_8=114688 \\ \\ a_n=a_1 \times r^{n-1} \\ a_8=a_1 \times r^7 \\ 114688=7 \times r^7 \\ \frac{114688}{7}=r^7 \\ 16384=r^7 \\ r=\sqrt[7]{16384} \\ r=4 \\ \\ S_n=\frac{a_1(1-r^n)}{1-r} \\ \Downarrow \\ S_8=\frac{7(1-4^8)}{1-4}=\frac{7(1-65536)}{-3}=\frac{7 \times (-65535)}{-3}=7 \times 21845=152915[/tex]

The answer is 152,915.

Answer:

152,915

Step-by-step explanation:

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