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

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Answer 1 · 2018-05-17T07:44:19

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

Formula for nth term $a_n = a r^(n-1)$

Given $a_2 = 3, a_5 = 3/64, n = 1$

To find first term ‘a’ as n = 1

$a_2 = a r^(2-1) = a r = 3$

$a_5 = a r^(5-1) = a r^4 = 3/64$

$a_5 / a_2 = (ar^4) / (a r) = r^3 = (cancel3/64)/cancel3 = 1/64$

$r^3 = (1/4^3), r = 1/4$

We know, $a_2 = a r = 3$

$:. a = 3/r = 3/(1/4) = 12$

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

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