What is the equation for a geometric sequence with a first term of 5 and a second term of −10?

an = 5(−2)n − 1
an = 5(2)n − 1
an = 5(−15)n − 1
an = 5(15)n − 1

Question

What is the equation for a geometric sequence with a first term of 5 and a second term of −10?

an = 5(−2)n − 1
 an = 5(2)n − 1
 an = 5(−15)n − 1
 an = 5(15)n − 1

byeeee · Answer

@dude

dude · Answer

Geometric sequences are written as 
$a_n=a_1\cdot r^{n-1}$
$a_1$ is the first term
$r$ is the rate

Do you have an idea on this?

byeeee · Answer

no not really besides that 5 is a1

dude · Answer

For this one we can work backwards, we know that the second term is -10 and the first term is 5, so...
$n$ is 2
$a_n=-10$
and $a_1=5$

$a_n=a_1\cdot r^{n-1}$
$-10=5\cdot r^{2-1}$
Combine the exponent
$-10=5\cdot r^{1}$
$r^1$ can be re-written as just $r$
$-10=5\cdot r$
Divide by 5 on both sides
$-2=r$

dude · Answer

Now we have all values
$a_1=5$
$r=-2$

So..
$a_n=5(-2)^{n-1}$

byeeee · Answer

oh

byeeee · Answer

ohh i see

byeeee · Answer

Thank you