# How do you find the first five terms of the geometric sequence a_1=576, r=-1/2?

Dec 13, 2016

See explanation

#### Explanation:

${a}_{1} = 576 {\left(- \frac{1}{2}\right)}^{0} = 576 \times \left(1\right) = + 576$

${a}_{2} = 576 {\left(- \frac{1}{2}\right)}^{1} = - 288$

${a}_{3} = 576 {\left(- \frac{1}{2}\right)}^{2} = + 144$

${a}_{4} = 576 {\left(- \frac{1}{2}\right)}^{3} = - 72$

${a}_{5} = 576 {\left(- \frac{1}{2}\right)}^{4} = + 36$

By observation, for any $i$ we have ${a}_{i} = 576 {\left(- \frac{1}{2}\right)}^{i - 1}$