# Consider a sequence of numbers given by the definition c_1=2, c_i=c_(i-1)*3, how do you write out the first 4 terms and how do you find the value of c_4-c_2?

Dec 24, 2016

${c}_{4} - {c}_{2} = 48$.

#### Explanation:

The terms can be obtained as follows.

${c}_{2} = {c}_{2 - 1} \cdot 3 = {c}_{1} \cdot 3 = 2 \cdot 3 = 6$

${c}_{3} = {c}_{3 - 1} \cdot 3 = {c}_{2} \cdot 3 = 6 \cdot 3 = 18$

${c}_{4} = {c}_{4 - 1} \cdot 3 = {c}_{3} \cdot 3 = 18 \cdot 3 = 54$

Thus, the value of ${c}_{4} - {c}_{2}$ is $54 - 6 = 48$.

Hopefully this helps!