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Sequences

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1. John wants to fence a 150 square meters rectangular field. He wants the length and width to be natural numbers {1,2,3,...}. What field dimensions will require the least amount of fencing?

2. List the terms that complete a possible pattern in each of the following, and classify each sequence as arithmetic, geometric, or neither:
(a) 38, 33, 28, 23, 18, ____, ____, ____
(b) 640, 320, 160, 80, ____, ____, ____

3. Find the following sum: 6 + 8 + 10 + 12 + ... + 100.

4. A special rubber ball is dropped from a height of 128 meters. Each time the ball bounces to half of its previous height. After 1 bounce the ball reaches a height of 64 meters.
(a) How high did the ball reach after the 7th bounce?
(b) How high does the ball reach after the nth bounce?

5. Use 3 and 4 as the first two terms of a Fibonacci-type sequence.
Find the next five terms:
3, 4, _______, _______, _______, _______, _______

6. Solve the following equations for x.
(a) 3x + 5 = 23
(b) 6(x - 8) = 2x + 12

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Solution Summary

This provides several examples of working with sequences, as well as a few examples of solving equations

Solution provided by:
Sandhya Sharma, MSc
Education
  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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