Question

Write an explicit formula for a1 = –2, an = an – 1 + 4, n ≥ 2.

Answer 1

The formula given is as follows

$a_{1}=-2, a_{n} = a_{n-1}+4, n\geq2$

Answer:

$a_{n} = 4n - 6$

Step-by-step explanation:

Since it is given that $n\geq 2$

$a_{2} = a_{1}+4$

$a_{3} = a_{2}+4$

... and so on...

we substitute $a_{1}$  to $a_{2}$ , $a_{2}$ to $a_{3}$ and so on.. we will get

$a_{3} = a_{2} + 4$

   $= a_{1} + 4 +4$

   $= a_{1} + 2(4)$

$a_{4} = a_{3} + 4$

$= a_{1} + 2(4) +4$

$= a_{1} + 3(4)$

and the patterns goes on.

We can see from the recursion pattern that

$a_{n} = a_{1} + (n-1)(4)$

$a_{n} = -2 + (n-1)(4)$

$= -2 + 4n - 4$

$= 4n - 6$