A geometric series

Tashalee

student

The sum of the first 3 terms of a geometric series is 13. The sum of their reciprocal is 13/9. how do you find the first three terms?

Hi Tashalee,

Since you have a geometric series the first three terms can be written

a, ar, ar²
for some numbers a and r. Thus you have

a + ar + ar² = 13
and

Multiplying the numerator and denominator br a gives

Since

a + ar + ar² = 13
a²r² = 9 and thus ar = 3 or a = ³/_r. Substitute into the above equation and solve for r.