What is the sum of a 7-term geometric series if the first term is 6, the last term is 24,576, and the common ratio is 4? Plz halp!!!

Question

rippedblue42 · Answer

Plz help!!!

loser66 · Answer

I forgot what geometric series is :(
Can you state it out?

rippedblue42 · Answer

What do you mean?

legomyego180 · Answer

Is this calc 2?

@loser66

A geometric series is a series in the form:
$$\sum_{k=a}^{\infty}(\frac{ a }{ b })^k$$
Where if $\frac{ a }{ b } > 1$ the series diverges, $\frac{ a }{ b } < 1$ converges.

The sum formula for a geometric series is:

$$\sum_{k=c}^{\infty}(\frac{ a }{ b })^k \rightarrow _{SUM}=\frac{ (\frac{ a }{ b } )^c}{ 1-\frac{ a }{ b } }$$

sshayer · Answer

$$S _{7}=6 \times \frac{ 4^7-1 }{ 7-1 }=?$$

sshayer · Answer

sum of  a geometric series with c.r r>1 is
$$S _{n}=a \times \frac{ r^n-1 }{ r-1 }$$
where a is first term ,n=number of terms
r=common ratio.

rippedblue42 · Answer

It's algebra 2

rippedblue42 · Answer

Is it 19,662?

rippedblue42 · Answer

Idk what do to with the common ratio

rippedblue42 · Answer

???

rippedblue42 · Answer

Oh wait. It'd be 32,766

loser66 · Answer

@legomyego180  thanks for the explanation :) 
I wish I get the answer from the Asker :)

faiqraees · Answer

$$\large\rm S_n=\frac{initial(1-ratio^{terms})}{1-ratio} $$