Answer:
that repeats after the third term, to find the fifth term we find the remainder of 5 divided by 3, which is 2. (5 ÷ 3 is 1 remainder 2).
The fifth term is then the same as the second term, which is y.
Example:
The first term in a sequence of numbers is 2. Each even-numbered term is 3 more than the previous term and each odd-numbered term, excluding the first, is –1 times the previous term. What is the 45th term of the sequence?
Solution:
Step 1: Write down the terms until you notice a repetition.
2, 5, -5, - 2, 2, 5, -5, -2, …
The sequence repeats after the fourth term. Step 2: To find the 45th term, find the remainder for 45 divided by 4, which is 1. (45 ÷ 4 is 11 remainder 1)
Step 3: The 45th term is the same as the 1st term, which is 2.
Answer: The 45th term is 2.
Number Sequence Problems: Determine The Pattern Of A Sequence
Example:
6, 13, 27, 55, …
In the sequence above, each term after the first is determined by multiplying the preceding term by m and then adding n. What is the value of n?
Solution:
Method 1:
Notice the pattern:
6 × 2 + 1 = 13
13 × 2 + 1 = 27
The value of n is 1.
Method 2:
Write the description of the sequence as two equations with the unknowns m and n, as shown below, and then solve for n.
6m + n = 13 (equation 1)
13m + n = 27 (equation 2)
Using the substitution method
Isolate n in equation 1
n = 13 – 6m
Substitute n = 13 – 6m into equation 2
13m + 13 – 6m = 27
7m = 14
m = 2
Substitute m = 2 into equation 1
6(2) + n = 13
n = 1
Answer: n = 1
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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