# How do you write the first five terms of the geometric sequence a_1=3, r=sqrt5?

Sep 4, 2017

$\left\{3 , 3 \sqrt{5} , 15 , 15 \sqrt{5} , 75\right\}$

#### Explanation:

a GP is generated by multiplying the previous term by the common ration.

Starting with the first term given.

${a}_{1} = 3$

${a}_{2} = 3 \times \sqrt{5} = 3 \sqrt{5}$

${a}_{3} = 3 \sqrt{5} \times \sqrt{5} = 3 \times 5 = 15$

${a}_{4} = 15 \times \sqrt{5} = 15 \sqrt{5}$

${a}_{5} = 15 \sqrt{5} \times \sqrt{5} = 15 \times 5 = 75$