Back to Exercise: Write arithmetic and geometric sequences

Exercises: Write Arithmetic and Geometric Sequences Recursively and Explicitly

Work through each section in order. For any sequence, always verify your formula by computing the first term.

Grade 9·21 problems·~28 min·Common Core Math - HS Functions·group·hsf-bf-a-2

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Warm-Up: Review What You Know

The sequence 4, 12, 36, 108, ... is best classified as:

Arithmetic — because the terms are increasing

Geometric — because consecutive terms have a constant ratio

Arithmetic — because the differences 8, 24, 72 are increasing by a factor of 3

Neither arithmetic nor geometric

For the arithmetic sequence 7, 11, 15, 19, ..., what is the common difference $d$ ?

For the geometric sequence 5, 10, 20, 40, ..., what is the common ratio $r$ ?

Fluency Practice

An arithmetic sequence has $a_1 = 3$ and $d = 5$ . Using the explicit formula $a_n = a_1 + (n-1)d$ , find $a_{10}$ .

A job pays $32,000 in year 1 with a $2,500 raise each year. Using the arithmetic explicit formula, what is the salary in year 8?

A geometric sequence has $a_1 = 2$ and $r = 3$ . Using the explicit formula $a_n = a_1 \cdot r^{n-1}$ , find $a_5$ .

A car worth $24,000 depreciates 20% per year. Which explicit formula gives its value after $n$ years?

$a_n = 24000 \cdot (0.2)^{n-1}$

$a_n = 24000 - 20n$

$a_n = 24000 \cdot (0.8)^{n-1}$

$a_n = 24000 \cdot (0.8)^n$

The explicit formula $a_n = 7 + (n-1) \cdot 4$ corresponds to a recursive definition with $a_1 = \text{\hspace{0.2em}\fbox{\phantom{000000}}\hspace{0.2em}}$ and $a_n = a_{n-1} + \text{\hspace{0.2em}\fbox{\phantom{000000}}\hspace{0.2em}}$ .

initial value a₁:

common difference d:

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