Solve by unfolding: a0=2, and, n>=1, a_n=7a_n-1.

1 answer:

6 0

We are told that the first term is 2. The next term is 7(2) = 14; the third term is 7(14) = 98. And so on. So, the first term and the common ratio (7) are known.

The nth term of this geometric series is a_n = 2(7)^(n-1).

Check: What is the first term? We expect it is 2. 2(7)^(1-1) = 2(1) = 2. Correct.

What is the third term? We expect it is 98. 2(7)^(3-1) = 2(7)^2 = 98. Right.<span />

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Answer:

The end of the flagpole is 50.79 ft away from the base of the pole.

Step-by-step explanation:

The problem is represented by the diagram below.

The broken flagpole forms the shape of a right angled triangle. We need to find one of the sides of the triangle, the adjacent (x).

The hypotenuse is the broken part of the flagpole (53 ft), while the opposite is the part of the flagpole that is still stuck to the ground (28 ft).

Using Pythagoras theorem, we have that:

$hyp^2 = adj^2 + opp^2$