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A tree in the Amazon rain forest grows an average of 2.3 cm per week. Write a sequence that represents the weekly height of the tree if it is 7 meters tall today. Write a recursive formula for the sequence and find the height of the tree after 6 weeks.

Answer :

Answer:

Recursive formula

= an = a1 +(n - 1)d

Where

a1 = First term

n = nth term

d = common difference

The height of the tree after 6 weeks = 711.5 centimeters or 7.115 meters

Step-by-step explanation:

Recursive formula

= an = a1 +(n - 1)d

Where

a1 = First term

n = nth term

d = common difference

We are told that the tree is 7 meters tall today = a1

We convert to centimeters

1m = 100cm

7m =

Cross Multiply

= 7 ร— 100cm

= 700cm

And it grows at an average of 2.3cm per week = 2.3

Hence, an = a1 +(n - 1)d

We are to find the height of the tree after 6 weeks

a6 = 700 + (6 - 1) 2.3

a6 = 700 + (5)2.3

a6 = 700 + 11.5

a6 = 711.5cm.

We can convert to meters if we like

= 100 cm = 1 m

711.5 cm =

711.5cm/100

= 7.115m

The height of the tree after 6 weeks is 711.5 cm or 7.11 meters

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