1. Use the explicit formula an = 4 − 3n to find the seventh term of the arithmetic sequence.

Question

A) a7 = −1
B) a7 = 1
C) a7 = −17
D) a7 = 7

2. Given the recursive formula for the geometric sequence a1 = 5, an = 2/5 an-1, find the second term of the sequence.
A) a2 = 2/5
B) a2 = 2
C) a2 = 5 2/5
D) a2 = 8/5

Answer 1

1. To find the seventh term of the arithmetic sequence with the explicit formula $a_n=4-3n$, we substitute $n=7$ into the formula:

$$a_7=4-3(7)$$ $$a_7=4-21$$ $$a_7=-17$$

So, the answer is C) a7 = −17.

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2. To find the second term of the geometric sequence with the given recursive formula $a_1=5$ and $a_n=\frac{2}{5}{a}_{n-1}$, we first calculate $a_2$:

$$a_2=\frac{2}{5}{a}_1$$ Substituting $a_1=5$:

$$a_2=\frac{2}{5}\times 5$$ $$a_2=2$$

So, the answer is B) a2 = 2.