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Algebra - Sequence Questions

Brackets [ ] are used to indicate a subscript, so a[n] means the nth term of a sequence.

1. Write the first four terms of the sequence defined by a[n] = 2n + 3.

2. Write the first four terms of the arithmetic sequence with a[1] = -6 and d = 4.

3. What is the common ration in the geometric sequence 4, -12, 36, -108, . . .?

4. Describe the pattern on the exponents of a and b in the expansion of (a + b)^n.

5. Explain the difference between a combination and a permutation.

Solution Preview

1. a[1] = 2 + 3 = 5
a[2] = 2*2 + 3 = 7
a[3] = 2*3 + 3 = 9
a[4] = 2*4 + 3 = 11

2. Arithmetic sequence has the formula:
a[n] = a[1] + (n-1)d
With a[1]= -6 and d =4, we can write the sequence as:
a[n]= -6 + 4*(n-1)
Hence a[1] = -6
a[2] = -6 + 4 = -2
a[3] = -6 +4*2 = 2
a[4] = -6 +4*3 = ...

Solution Summary

The solution provides detailed explanations and step-by-step instructions for each of these algebra problems.

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