The third term of geometric progression is 5 and the 6th term is -40. find the 8...

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sanchezjhayem123 @sanchezjhayem123

October 2022 1 1 Report

The third term of geometric progression is 5 and the 6th term is -40. find the 8th term.

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luna3473

Answer:

The 8th term of the Geometric Progression is -160.

Step-by-step explanation:

→LET US FIND FIRST THE RATIO TO DETERMINE THE SEQUENCE.

FORMULA:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \green{\boxed{an = a1 {r}^{n - 1}}}$

GIVEN:

→ LET US SAY THAT THE 3RD TERM IS THE FIRST TERM AND THE 6TH TERM IS THE 4TH TERM.

$\: \: \: \: \: \: \: \: a1 = 5 - \: the \: first \: term \: \:$

$\: \: \: \: \: \: \: an = - 40 - \: the \: last \: term$

$\: \: \: \: \: \: \: \: \: n = 4 - \: the \: no. \: of \: terms$

SUBSTITUTE:

$\: \: \: \: \: \: \: \: \: \: \: \: - 40 = 5 {r}^{4 - 1}$

SOLVE:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{ - 40}{5} = \frac{5}{5} {r}^{4}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 8 = {r}^{4}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \sqrt[3]{ - 8} = \sqrt[3]{ {r}^{3} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{\boxed{- 2 = r}}$

GEOMETRIC SEQUENCE:

→ NOW THAT YOU KNOW THE RATIO IS -2, YOU CAN NOW DETERMINE THE GEOMETRIC PROGRESSION BY MULTIPLYING IT.

$\: \:\green{\boxed{ \frac{5}{4}, \: - \frac{5}{2} , \: 5 , \: - 10 , \:20 ,\: \: - 40 , \: 80 ,\: \: - 160}}$

#CarryonLearning

sanchezjhayem123 Thank you so much

trixiaeunice hey luna 3473 can you answer this 1. CJ gratuated from elementary 5 years ago what is 5 years aho positive or negative?

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Answers & Comments

The 8th term of the Geometric Progression is -160.

FORMULA:

GIVEN:

SUBSTITUTE:

SOLVE:

GEOMETRIC SEQUENCE:

#CarryonLearning

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