Question

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

{ f(0)=30
{f(n+1)= f(n)+7

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

You can earn up to 3 points, 1 for each correct value/variable in the equation.

Format: Y=_________

Answer 1

Answer:

Y(n) = 7n + 23

Step-by-step explanation:

Given:

f(0) = 30

f(n+1) = f(n) + 7

For n=0 : f(1) = f(0) + 7

For n=1 :  f(2) = f(1) + 7

For n=2 : f(3) = f(2) + 7 and so on.

Hence the sequence is an arithmetic progression with common difference 7 and first term 30.

We have to find a general equation representing the terms of the sequence.

General term of an arithmetic progression is:

T(n) = a + (n-1)d

Here a = 30 and d = 7

Y(n) = 30 + 7(n-1) = 7n + 23