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In-s [12.5K]
3 years ago
8

Find the nth term -1 8 19 32 47

Mathematics
1 answer:
koban [17]3 years ago
4 0

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

<u>Step-by-step explanation:</u>

-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}

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