Question

In a geometric series,
a2=6
a5=48

Which is the first term, which is the constant and write the progression

Answer 1

I know that
\[an=a1*r ^{n-1}\]
What goes next?

Answer 2

6=a1*r^(n-1) ?

Answer 3

6=a1*r^(2-1), 6=a1*r

Answer 4

As you said :
\[a_n=a_1\times q^{n-1}\]
where q is the constant of the serie, so we have :
\[a_2=a_1\times q\\a_5=a_1\times q^4\]
Is that true ?

Answer 5

Yep

Answer 6

so we get :
\[6=a_1\times q~~~~~~(1)\\48=a_1\times q^4~~~(2)\]
Now, we can divide the equation (2) over (1) , what should we get ?

Answer 7

8=q^3, q=2!

Answer 8

Good. Now the 1st term can be found easily, can't it ?

Answer 9

yepp :D

Answer 10

3 :) thanks

Answer 11

So an=3*2^n-1 ?

Answer 12

Yes, it is ! And you are welcome !