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When a certain tree was planted, it was 4ft tall, and the [#permalink]

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When a certain tree was planted, it was 4ft tall, and the height of the tree increased by a constant amount each year for 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

When a certain tree was planted, it was 4ft tall, and the height of the tree increased by a constant amount each year for 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

(a) 3/10 (b) 2/5 (c) 1/2 (d) 2/3 (e) 6/5

How do I go about solving? Thanks in advance.

Answer is D

Planted ==> 4 ft
1st year ==> 4 + x
2nd year ==> 4 + x +x ==> 4 + 2x
..
...
4th year ==> 4 + 4x
6th year ==> 4 + 6x

(6/5)(4+4x) = (4+6x)
x = 2/3
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When a certain tree was planted, it was 4ft tall, and the height of the tree increased by a constant amount each year for 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

(a) 3/10 (b) 2/5 (c) 1/2 (d) 2/3 (e) 6/5

How do I go about solving? Thanks in advance.

The sequence is {4,4+x,4+2x,4+3x,4+4x,4+5x,4+6x}
Given that ht in 6th year = ht in 4th year + 1/5(ht in 4th year),
=>(4 + 6x) = (4+4x) + (4+4x)/5 (4th year height
Solving we get x = 2/3

First planted: 4 ft
First year = increase by x ft
Second year = increase by x ft
... and so on...
So by end of 6 years, the tree would be 4 + 6x ft tall