Please answer properly
Guide Questions:
1. How did you determine the indicated term?
2. What kind of sequence are the above sequences?
3. How important is the role of the common ratio in determining the
indicated term?
4. How do you call the terms between the first and the last terms?
5. Can you find the sum of the above sequence?
Guide Questions:
1. How did you determine the indicated term?
2. What kind of sequence are the above sequences?
3. How important is the role of the common ratio in determining the
indicated term?
4. How do you call the terms between the first and the last terms?
5. Can you find the sum of the above sequence?
Answers & Comments
Answer:
1. To find the indicated term, we have to apply the indicated number instead of n. For example, if we want to find 5th term of the sequence, we have to apply 5 instead of n in the nth term of the sequence.
2. Types of Sequence and Series
Arithmetic Sequences. Geometric Sequences. Harmonic Sequences. Fibonacci Numbers.
3. The behavior of a geometric sequence depends on the value of the common ratio. If the common ratio is: Positive, the terms will all be the same sign as the initial term. ... Less than −1 , for the absolute values there is exponential growth toward positive and negative infinity (due to the alternating sign)
4. Finite and Infinite Sequences
Since the sequence has a last term, it is a finite sequence. Infinite sequence: {4,8,12,16,20,24,…} The first term of the sequence is 4
5. The sum of an arithmetic series is found by multiplying the number of terms times the average of the first and last terms. Example: 3 + 7 + 11 + 15 + ··· + 99 has a1 = 3 and d = 4. To find n, use the explicit formula for an arithmetic sequence.