SOLUTION: given two terms in a geometric sequence find the term named in the problem and the explicit formula http://prntscr.com/s9icre

Question 1157839: given two terms in a geometric sequence find the term named in the problem and the explicit formula
http://prntscr.com/s9icre
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

#24....

For any geometric sequence,

The formula says exactly what the definition of a geometric sequence says: the n-th term is the first term, multiplied by the common ratio, r, (n-1) times.

Note it is (n-1) times, because the first term is multiplied by the common ratio 0 times.

Formally, divide a(5) by a(4):

Informally, simply observe that the 5th term is the 4th term multiplied by the common ratio; 48/24 = 2.

We have determined r; to finish finding the explicit formula, we need to find a(0).

The explicit formula is

Evaluate a(9) using the formula.

Or, informally, multiply the 5th term, 48, by 2, 4 more times....

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

23.
a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio
We can also calculate any term using the Rule:

given:
->

........solve for
......eq.1

->

........solve for
......eq.2

from eq.1 and eq.2 we have

.......cross multiply
.....both sides divide by

go to
......eq.2, substitute

nth term formula is:

find ->

24.

given:
->

.....eq.1
->

.....eq.2
from eq.1 and eq.2 we have

.....eq.2, plug in

then,

find ->

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