1. Find the first six terms of the sequence.a1 = 4, an = an-1 + 8 For this case, the first thing you should do is replace the values given one by one. We have then: a1 = 4 a2 = a1 + 8 = 4 + 8 = 12 a3 = a2 + 8 = 12 + 8 = 20 a4 = a3 + 8 = 20 + 8 = 28 a5 = a4 + 8 = 28 + 8 = 36 a6 = a5 + 8 = 36 + 8 = 44 Answer: C) 4, 12, 20, 28, 36, 44
2. Find the first six terms of the sequence. a1 = -8, an = 5 an-1 For this case, the first thing you should do is replace the values given one by one. We have then: a1 = -8, a2 = 5 ^ (- 8) = -40 a3 = 5 ^ (- 40) = -200 a4 = 5 ^ (- 200) = -1000 a5 = 5 ^ (- 1000) = -5000 a6 = 5 ^ (- 5000) = -25000 answer: A) -8, -40, -200, -1000, -5000, -25,000
3. Find an equation for the nth term of the arithmetic sequence. 8, 6, 4, 2, ... What you must do for this case is to verify which sequence is best suited to the problem. For this case we have: 8, 6, 4, 2, The sequence is: an = 8 + -2 (n - 1) a1 = 8 + -2 (1 - 1) = 8 a2 = 8 + -2 (2 - 1) = 6 Answer: An equation for the nth term of the arithmetic sequence is D) an = 8 + -2 (n - 1)
4. Find an equation for the nth term of the arithmetic sequence. -17, -12, -7, -2, ... What you must do for this case is to verify which sequence is best suited to the problem. For this case we have: -17, -12, -7, -2, The sequence is: an = -17 + 5 (n - 1) a1 = -17 + 5 (1 - 1) = - 17 a2 = -17 + 5 (2 - 1) = - 12 Answer: Answer: An equation for the nth term of the arithmetic sequence is C) an = -17 + 5 (n - 1)
5. Find an equation for the nth term of the arithmetic sequence. a19 = -58, a21 = -164 What you must do for this case is to verify which sequence is best suited to the problem. For this case we have: a19 = -58, a21 = -164 The sequence is: an = 896 - 53 (n - 1) a19 = 896 - 53 (19 - 1) = - 58 a21 = 896 - 53 (21 - 1) = - 164 Answer: An equation for the nth term of the arithmetic sequence is B) an = 896 - 53 (n - 1)
6. A certain species of tree grows an average of 0.5 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 200 centimeters tall.
For this case, what you should do is to write the equation step by step to find the correct result. We have then: the measurements begin when the tree is 200 centimeters tall 200 tree grows an average of 0.5 cm per week 200 + 0.5n Where n: number of weeks. answer: An equation for the sequence that represents the weekly height of this tree in centimeters is an = 200 + 0.5n
