Mathematics: In a geometric sequence, a4=54 and a7=1458. what is the 12th term? a. 5,616 b. 354,294 c. 14,350,365 d. 234,812,358

In a geometric sequence, a4=54 and a7=1458. what - id454714582913901, kingkuka1700

Ответ:

gungamer720

05.01.2022

A7 / a4 = r^(7-4) = r^3 where r = common ratio
so r^3 = 1458 / 54 = 27

r = 3

12th term = a7 * r^5 = 1458* 3^5 = 354,294

Note r could also be -3 but not in this case because 12th term is positive

Its b

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Ответ:

190145

05.01.2022

Mathematics

Answer-

$\boxed{\boxed{a_{12}=354294}}$

Solution-

If there are 2 terms of a Geometric Sequence a_n and a_k where (n > k), then

$a_n=a_k\cdot r^{n-k}$

where, r = common ration of the G.P.

Here,

$a_4 = 54\\\\a_7=1458$

Putting in the equation,

$\Rightarrow a_7=a_4\cdot r^{7-3}$

$\Rightarrow a_7=a_4\cdot r^3$

$\Rightarrow 1458=54\cdot r^3$

$\Rightarrow r^3=\dfrac{1458}{54}$

$\Rightarrow r^3=27$

$\Rightarrow r=3$

Again putting the values in the equation,

$\Rightarrow a_{12}=a_7\cdot r^{12-7}$

$\Rightarrow a_{12}=a_7\cdot r^5$

$\Rightarrow a_{12}=1458\cdot 3^5$

$\Rightarrow a_{12}=354294$

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Ответ:

elijahmaderos25491

03.06.2020

Mathematics

step-by-step explanation:

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In a geometric sequence, a4=54 and a7=1458. what is the 12th term?
a. 5,616
b. 354,294
c. 14,350,365
d. 234,812,358

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