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7. Find and solve a recurrence relation for p_n, the value of a stock market indicator...

7. Find and solve a recurrence relation for p_n, the value of a stock market indicator that obeys the rule that the change this year (from the previous year) equals twice last year’s change. Suppose p_0 = 1, p_1 = 4.

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Answer #1

The value of the stock this year changed by two times that of the last year. Hence the change this year .

Take . Then and for . So is a geometric progression with first term 3. Therefore .

Now

Using the formula for a sum of a geometric progression we have

.

Hence .

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