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3 years ago

HELME PLEASE I WILL MARK THE BRAINEST

Mathematics

1 answer:

Lina20 [59]3 years ago

5 0

Answer:C

Step-by-step explanation:i would say C because its not a negative and it dosent go up 2 let me know if im wrong

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Find S9, the sum of the geometric series to the 9th term, in which a3=3.645 and a8=15

ArbitrLikvidat [17]

Answer:

The sum of the first nine terms of the sequence is 74.44.

Step-by-step explanation:

Geometric sequence concepts:

The nth term of a geometric sequence is given by the following equation.

$a_{n+1} = ra_{n}$

In which r is the common ratio.

This can be expanded for the nth term in the following way:

$a_{n} = a_{1}r^{n-1}$

In which $a_{1}$ is the first term.

Or even:

$a_{n} = a_{m}r^{n-m}$

The sum of the first n terms of a geometric sequence is given by:

$S_{n} = \frac{a_{1}(1 - r^{n})}{1 - r}$

Finding the common ratio:

$a_{3} = 3.645, a_{8} = 15$

$a_{n} = a_{m}r^{n-m}$

$a_{8} = a_{3}r^{8-3}$

$a_{3}r^{5} = a_{8}$

$3.645r^{5} = 15$

$r^{5} = \frac{15}{3.645}$

$r = \sqrt[5]{\frac{15}{3.645}}$

$r = 1.327$

Finding the first term:

$a_{3} = a_{1}r^{2}$

$a_{1} = \frac{a_{3}}{r^{2}}$

$a_{1} = \frac{3.645}{(1.327)^{2}}$

$a_{1} = 2.07$

Sum of the first nine terms:

$S_{9} = \frac{2.07*(1 - (1.327)^{9})}{1 - 1.327} = 74.44$

The sum of the first nine terms of the sequence is 74.44.

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