Arithmetic sequence

Writing terms of arithmetic sequences

100

Consecutive even numbers: in a sequence of consecutive even numbers, what is the 7th term?

the 7th term is 14.

200

Arithmetic sequence: what is the 12th term of the arithmetic sequence with first term -3 and common difference 4?

-3 + 4(12 - 1) = -3 + 44 = 41

500

Find the term: In an arithmetic sequence, the 4th term is 17 and the 9th term is 42. What is the 20th term?

97

1000

Find the position: In an arithmetic sequence with first term 7 and common difference 6, which term equals 223?

it is the 37th term

Recursive formula for an arithmetic sequence.

100

Recursive Formula: What is the recursive formula for an arithmetic sequence with first term -3 and common difference 4?

a_n = -3 + 4 (n - 1)

200

Recursive formula calculations: For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence.

a₁=39; a_n=a_n-1− 3

Answer: 𝑎_𝑛 = 39 - 3(𝑛 - 1) for n = 1, 2, 3, 4, 5, therefore, 36,33,30,27

500

Recursive Formula: What is the recursive formula for the arithmetic sequence where the nᵗʰ term is the average of the previous two terms plus 4?

Answer: a_n=(a_n-1 + a_n-2) / 2 + 4 

1000

Write a recursive formula for the arithmetic sequence. a = {−0.52, −1.02, −1.52, ...}

a_n=a_n-1 - 0.5

Explicit formula for an arithmetic sequence.

100

Explicit Formula What is the explicit formula for an arithmetic sequence with first term -6 and common difference 8?

a_n = -3 + 4(n - 1)

200

Analyze the Explicit Formula Write down the standard form of an explicit formula for an arithmetic sequence and explain each term.

The formula 𝑎_𝑛=𝑎₁+𝑑(𝑛−1). The terms in the formula are defined as follows:

1. 𝑎_𝑛: The nth term in the arithmetic sequence.
2. 𝑎₁: The first term in the arithmetic sequence.
3. 𝑑: The common difference between consecutive terms in the arithmetic sequence.
4. 𝑛: The position of the term in the arithmetic sequence.
5. (𝑛−1): The number of terms that come before the nth term in the sequence.

500

Find the 6th term An arithmetic sequence starts with a₁ = 8 and has a common difference of d = 5. What is the 6th term in the sequence?

𝑎_𝑛=8 + 5(6-1) = 8 + 25 = 33

1000

Construction: A construction project requires digging a trench that is 5 meters deep and 20 meters long. The trench is dug 3 meters each day. What is the explicit formula for the trench's depth after n days?

The explicit formula is: D(n)=5+3(n-1)