Find the 2nd, 3rd, and 5th terms of a geometric sequence having 1st term 8 and 4th term 27.

Question

campbell_st · Answer

if you are finding a term in a geometric series you can use 

$$T_{n} = ar^{n-1}$$

you know  the 1st term a = 8 and you will need to frind r, 

you also know the 4th term 27

so using the formula you have 


$$27 = 8r^{4-1}$$

divide both sides by 8

$$\frac{27}{8} = r^3$$

to find r take the cube root of both sides of the equation. 

When you have r you will be able to find the 2nd and 3rd terms.

anonymous · Answer

Alright! So I got that r=3/2... but I'm unsure as to where to go from there. Do we do the same thing (isolate r) to the other known term (a=8)?

campbell_st · Answer

ok... so the 2nd term n = 2

$$T_{2} = 8 \times (\frac{3}{2})^{2 - 1}$$

for the 3rd term n = 3

so substitute that and evaluate


and the 5th term is n = 5, substitute and evaluate

anonymous · Answer

Wow... that's so simple now that you've explained it!! Thank you again, so so much!! :)