osanseviero 2 years ago In a geometric series, a2=6 a5=48 Which is the first term, which is the constant and write the progression

1. osanseviero

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

2. osanseviero

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

3. osanseviero

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

4. anonymous

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 ?

5. osanseviero

Yep

6. anonymous

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 ?

7. osanseviero

8=q^3, q=2!

8. anonymous

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

9. osanseviero

yepp :D

10. osanseviero

3 :) thanks

11. osanseviero

So an=3*2^n-1 ?

12. anonymous

Yes, it is ! And you are welcome !