how can I solve for the first term when given the sum and the common ratio?
ex: the sum in a finite geometric series is 39,360 and the common ratio is three. What is the first term?
how can I solve for the first term when given the sum and the common ratio?
ex: the sum in a finite geometric series is 39,360 and the common ratio is three. What is the first term?
I think the sum of your geometric series should be:39,366 NOT 39,360.
If that is the case, then the 1st. term is: 2. Because:
2 x 3^9=39,366. So, the series will look like this:
2, 6, 18, 54, 162, 486, 1,458, 4,374, 13,122, 39,366........
+130536 We would have to know how many terms we have to give a precise answer.
The general form for a geometric sum, S, is given by;
S = a1 [ 1 - r^n] / [ 1 - r] where a1 is the first term, r is the common ratio, and n is the number of terms
Notice, however that
39360 = a1 [ 1 - 3^n] / [ 1 - 3] is true for n= 2 when a1 = 9840
But it's also true for n= 4 when a1 = 984
And it's also true for n = 8 when a1 = 12
In fact, we could generate an endless list of possible first terms depending upon our choices for n !!!
