# How do you write the expression for the nth term of the geometric sequence a_2=3, a_5=3/64, n=1?

May 17, 2018

color(crimson)(a_n = a_1 = a = 12

#### Explanation:

Formula for nth term ${a}_{n} = a {r}^{n - 1}$

Given ${a}_{2} = 3 , {a}_{5} = \frac{3}{64} , n = 1$

To find first term ‘a’ as n = 1

${a}_{2} = a {r}^{2 - 1} = a r = 3$

${a}_{5} = a {r}^{5 - 1} = a {r}^{4} = \frac{3}{64}$

${a}_{5} / {a}_{2} = \frac{a {r}^{4}}{a r} = {r}^{3} = \frac{\frac{\cancel{3}}{64}}{\cancel{3}} = \frac{1}{64}$

${r}^{3} = \left(\frac{1}{4} ^ 3\right) , r = \frac{1}{4}$

We know, ${a}_{2} = a r = 3$

$\therefore a = \frac{3}{r} = \frac{3}{\frac{1}{4}} = 12$

Hence, color(crimson)(a_n = a_1 = a = 12