Question

Question 17
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Find the sum of the first 10 terms of the following geometric sequences:
{3, 6, 12, 24, 48...}
3069
3066
O
3072
O 3075

Answer 1

Answer:

$S_{10} = 3069$

Step-by-step explanation:

Given

$Sequence = \{3, 6, 12, 24, 48...\}$

Required

Determine the sum of the first terms

First, we calculate the common ratio (r)

$r = \frac{T_2}{T_1}$

$r = \frac{6}{3}$

$r = 2$

The required sum is:

$S_n = \frac{a(r^n-1)}{r-1}$

Substitute 3 for a, 2 for r and 10 for n

$S_{10} = \frac{3(2^{10}-1)}{2-1}$

$S_{10} = \frac{3(1024-1)}{2-1}$

$S_{10} = \frac{3(1023)}{2-1}$

$S_{10} = \frac{3(1023)}{1}$

$S_{10} = \frac{3069}{1}$

$S_{10} = 3069$