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

Answer 1

@dude

Answer 2

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?

Answer 3

no not really besides that 5 is a1

Answer 4

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
\(-2=r\)

Answer 5

Now we have all values
\(a_1=5\)
\(r=-2\)

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

Answer 6

oh

Answer 7

ohh i see

Answer 8

Thank you