Question

write a recursive formula and an explicit formula for the following arithmetic sequence 16,23,30,37,44

Answer 1

16, 23, 30, 37, 44

We can note from the sequence that every number is the previous one plus 7, then the recursive formula will be.

`a_n=a_(n-1)+7`

for all n greater or equal that 2 because the first term a1=16. Now let's deduce the explicit formula

`a_1=16`
`a_2=a_1+1(7)`
`a_3=30=16+2(7)=a_1+2(7)`

at this point we can see the pattern, for the nth term, you add to the first term 7 multipied by (n-1), then the explicit formula is

`a_n=16+(n-1)7`

simplifying

`a_n=9+7n`