Question

if $a_{1}$=4 and $a_{n}$= $5a_{n-1}$-1 then find the value of $a_{3}$

Answer 1

Answer:  94

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Explanation:

The first term is 4 because of the notation $a_1 = 4$

To get the second term, we'll use the recursive equation $a_n = 5(a_{n-1})-1$ which basically says $\text{nth term} = 5*(\text{previous term})-1$. To get the second term, we'll multiply the first term by 5, then subtract off 1.

2nd term = 5*(1st term) - 1

2nd term = 5*4 - 1

2nd term = 19

This means $a_2 = 19$

We repeat this process again to find the third term $a_3$

$a_n = 5*(a_{n-1})-1\\\\a_3 = 5*(a_{3-1})-1\\\\a_3 = 5*(a_{2})-1\\\\a_3 = 5*(19)-1\\\\a_3 = 95-1\\\\a_3 = \boldsymbol{94}$

The third term is 94