How do you write the expression for the nth term of the geometric sequence $a_{1} = 64, r = - \frac{1}{4}, n = 10$ $a_1=64, r=-1/4, n=10$ ?

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How do you write the expression for the nth term of the geometric sequence $a_{1} = 64, r = - \frac{1}{4}, n = 10$ $a_1=64, r=-1/4, n=10$ ?

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Answer 1 · 2017-07-25T08:39:07

$\frac{256}{5} (1 - {(- \frac{1}{4})}^{n})$ $256/5(1-(-1/4)^n)$

Explanation:

$the nth term for a geometric sequence is$ $"the nth term for a geometric sequence is"$

$∙ x a_{n} = \frac{a (1 - r^{n})}{1 - r} \leftarrow a = a_{1}$ $•color(white)(x)a_n=(a(1-r^n))/(1-r)larra=a_1$

$\Rightarrow a_{n} = \frac{64 (1 - {(- \frac{1}{4})}^{n})}{1 + \frac{1}{4}}$ $rArra_n=(64(1-(-1/4)^n))/(1+1/4)$

$\Rightarrow a_{n} = \frac{256}{5} (1 - {(- \frac{1}{4})}^{n})$ $color(white)(rArra_n)=256/5(1-(-1/4)^n)$

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How do you write the expression for the nth term of the geometric sequence $a_{1} = 64, r = - \frac{1}{4}, n = 10$ $a_1=64, r=-1/4, n=10$ ?

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How do you write the expression for the nth term of the geometric sequence a_1=64, r=-1/4, n=10a1=64,r=−14,n=10a_1=64, r=-1/4, n=10?

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How do you write the expression for the nth term of the geometric sequence $a_{1} = 64, r = - \frac{1}{4}, n = 10$ $a_1=64, r=-1/4, n=10$ ?