Question

At the beginning of spring, Taylor planted a small sunflower in her backyard. When it was first planted, the sunflower was 25 inches tall. The sunflower then began to grow at a rate of 2 inches per week. How tall would the sunflower be after 7 weeks? How tall would the sunflower be after w weeks?

Answer 1

Height after w weeks: 23+2w

Height after 10 weeks: 37

Answer 2

Explanation:

The sunflower then began to grow at a rate of 2 inches per week. This means that the rate of growth of the sunflower is in arithmetic progression. We would apply the formula for determining the nth term of an arithmetic sequence which is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 25 inches

d = 2 inches

To determine the height after 7 weeks, T7

n = 7

T7 = 25 + 2(7 - 1)

T7 = 25 + 12

T7 = 37 inches

To determine the height after w weeks, Tw

n = w

Tw = 25 + 2(w - 1)

Tw = 25 + 2w - 2

Tw = 23 + 2w