Question

Find the nth term -1 8 19 32 47

Answer 1

`\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_(-1)+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6`

Explanation:

-1 → 8 = +9

8 → 19 = +11

19 → 32 = +13

32 → 47 = + 15

a₁ = -1

d = 2n + 5

Recursive formula is: the previous term plus the difference (d)

`\large\boxed{a_n=a_(n-1)+2n+5}`

Explicit formula is the first term plus the product of d and n-1:

`a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}`