Question

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