Sequences and Series: Algebra 2 Math Test – PDF Download

Question 1: Sequence from a graph (2 points)

The graph shows the first four terms of a sequence.

1. Write an explicit formula for \(a_{n}\). (1 point)
2. Find \(a_{30}\). (1 point)

Question 2: Alternating sequence (2 points)

A sequence begins \(6,\,-12,\,24,\,-48\), and each term is found the same way from the one before it.

1. Write an explicit formula for \(a_{n}\). (1 point)
2. Find \(a_{9}\). (1 point)

Question 3: Recursive to explicit (2 points)

A sequence is defined by \(a_{1}=9,\quad a_{n}=a_{n-1}-4\).

1. List the first four terms. (1 point)
2. Write an explicit formula and find \(a_{25}\). (1 point)

Question 4: Sigma evaluation (2 points)

Consider \(\sum_{k=1}^{6}(2k+3)\).

1. Write out all the terms. (1 point)
2. Find the sum. (1 point)

Question 5: Lecture hall (2 points)

A lecture hall has 20 rows. Row 1 has 12 seats and every row has 3 more seats than the row before it.

1. How many seats are in row 20? (1 point)
2. How many seats are in the hall? (1 point)

Question 6: Series with negative ratio (2 points)

Evaluate \(\sum_{k=1}^{8}3(-2)^{k-1}\).

Question 7: Missing terms (2 points)

A geometric sequence of positive terms has \(a_{4}=24\) and \(a_{6}=96\).

1. Find the common ratio and \(a_{1}\). (1 point)
2. Find \(a_{8}\). (1 point)

Question 8: Growing deposits (3 points)

Aisha deposits $100 into a savings jar in month 1 and increases the deposit by $15 each month after that. The chart shows the first four months.

1. Find her deposit in month 24. (1 point)
2. Find the total she has deposited after 24 months. (2 points)

Question 9: Loan amount (3 points)

Liam repays a loan with 24 monthly payments of $400. The interest rate is 0.5% per month, so a payment made \(k\) months from now is worth \(400(1.005)^{-k}\) today. The amount borrowed equals the value today of all 24 payments.

1. Write the amount borrowed in sigma notation. (1 point)
2. Find the amount borrowed to the nearest cent. (1 point)
3. Find the total interest Liam pays. (1 point)

⬇ Download the Algebra 2 Sequences and Series test (PDF, 88 KB)

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