Question 865729
The first term is -16. So a = -16



The common ratio is 12/(-16) = -3/4. You find this by dividing any term by it's previous term. It helps to keep the common ratio as a fraction. So r = -3/4



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We know a = -16 and r = -3/4. Because |r| < 1 is true, we know that the infinite geometric series converges to some fixed number (and it doesn't diverge).



We find this sum using the formula



S = a/(1 - r)



S = (-16)/(1 - (-3/4)) ... plug in a = -16 and r = -3/4



S = (-16)/(1 + 3/4)



S = (-16)/(4/4 + 3/4)



S = (-16)/(7/4)



S = (-16)*(4/7)



S = <font color="red">-64/7</font>



This means -16+12-9+... = <font color="red">-64/7</font>



Note: -64/7 = -9.14285714285714 approximately, but it's always a better idea to stick to the exact answer. This is because it's easier to get the approximate answer from the exact (it's usually harder to go from approximate to exact).