Ch. 8 - Sequences, Induction, and Probability
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- In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 7n - 4
Problem 1
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a₁ = 200, d = 20
Problem 1
- In Exercises 1–8, write the first five terms of each geometric sequence. a1 = 5, r = 3
Problem 1
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3n+2
Problem 1
- In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 1/(n - 1)!
Problem 3
- In Exercises 1–8, write the first five terms of each geometric sequence. a1 = 20, r = 1/2
Problem 3
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3^n
Problem 3
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= -8, d=5
Problem 4
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a1 = 300, d= -90
Problem 5
- In Exercises 1–8, write the first five terms of each geometric sequence. an = - 4a_(n-1), a1 = 10
Problem 5
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−3)^n
Problem 5
- Evaluate 40!/(4! 38!)
Problem 7
- In Exercises 1–14, write the first six terms of each arithmetic sequence. a1= 5/2, d = -1/2
Problem 7
- In Exercises 1–8, write the first five terms of each geometric sequence. an = - 5a_(n-1), a1 = - 6
Problem 7
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n(n+3)
Problem 7
- In Exercises 8–9, find each indicated sum. This is a summation, refer to the textbook.
Problem 8
- In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 +6, a₁ = −9
Problem 9
- In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r. Find a8 when a1 = 6, r = 2
Problem 9
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=2n/(n+4)
Problem 9
- In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. 1/3 + 2/4 + 3/5 + ... + 15/17
Problem 10
- In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -10, a₁ = 30
Problem 11
- In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r. Find a12 when a1 = 5, r = - 2
Problem 11
- In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n+1/(2^n−1)
Problem 11
- In Exercises 1–14, write the first six terms of each arithmetic sequence. an = an-1 -0.4, a₁ = 1.6
Problem 13
- In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r. Find a40 when a1 = 1000, r = - 1/2
Problem 13
- The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=7 and a_n=a_n-1 + 5 for n≥2
Problem 13
- In Exercises 12–15, write the first six terms of each arithmetic sequence. a1 = 3/2, d = -1/2
Problem 14
- In Exercises 15–22, find the indicated term of the arithmetic sequence with first term, and common difference, d. Find a6 when a₁ = 13, d = 4.
Problem 15
- In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r. Find a8 when a1 = 1 000 000, r = 0.1
Problem 15
- The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=3 and a_n=4a_n-1 for n≥2
Problem 15