Question

To describe a specific arithmetic sequence, Elijah wrote the recursive formula:

Write a linear equation that models this sequence using the sketchpad below.

Answer 1

Answer:

$t_{n}  = 30 + 7n$, where, n = 0, 1, 2, 3, 4, .........

Step-by-step explanation:

Given the arithmetic sequence in recursive formula.

f(0) = 30 and f(n + 1) = f(n) + 7 ......... (1)

Therefore, putting n = 0 in equation (1) we get f(1) = f(0) + 7 = 30 + 7 = 37 {Since, f(0) is given to be 30}

Again, putting n = 1 in equation (1) we get f(2) = f(1) + 7 = 37 + 7 = 44

And, putting n = 2 in equation (1) we get f(3) = f(2) + 7 = 44 + 7 = 51

and so on.

Therefore, the arithmetic sequence is 30, 37, 44, 51, .......

Therefore, the linear equation of this sequence is given by $t_{n}  = 30 + 7n$, where, n = 0, 1, 2, 3, 4, .........

(Answer)