Geometric sequence question? S11= 779..S12=890. what is s13? please show work use formula?

Hi

Sn = S1 * q^(n-1)

More easy

Sn+1 / Sn = q

S13 / S12 = S12 / S11

S13 = S12^2 / S11 = 890^2 / 779 = (2*5*89)^2 / (19*41)

Not simplifiable fraction

S13 = 792100/779

I got an answer using Excel's GoalSeek:

r = about 1.08353846629

The term and sums are:

1 45.9235 45.9235

2 49.7599 95.6835

3 53.9168 149.6002

4 58.4209 208.0211

5 63.3013 271.3224

6 68.5894 339.9118

7 74.3192 414.2311

8 80.5278 494.7589

9 87.2549 582.0138

10 94.5441 676.5579

11 102.4421 779.0000

12 111.0000 890.0000

13 120.2728 1010.2728

Sorry, I don't have a formulaic solution All I get is:

A12 = S12 - S11 = 890 - 779 = 111

A12 = A1(r^11) so A1 = A12/r^11

A1(1 + r + r^2 + ... + r^11) = A12/r^11 x (1 - r^12)/(1 - r) = S12

111(1 - r^12)/(r^11(1-r)) = 890

But I don't know how to solve directly for r.

I think railrule and Renie are assuming that the TERMS of the sequence are 779 and 890. Those are the SUMS of the first 11 or 12 terms, not the terms, right?

The ratio of consecutive sums doesn't give you much useful information.

And there is no way that 988 is the 13th sum. I think you messed up in typing the question. 988 makes 12th and 13 term 111 and 98, the ratio is therefore 0.882882883

If you back into the rest of the terms, they are

436.9069094

385.7376317

340.5611523

300.6756119

265.4613511

234.3712829

206.922394

182.6882397

161.2923197

142.4022282

125.7244898

111.0000

98.0000

and the sum is close to 3000.

So it looks like there are serious mistakes in your question.