Question

given the arithmetic sequence, {aₙ} = {7n + 8}, list the first four terms, and the common difference, d. the common difference: d = a₁ = a₂ = a₃ = a₄ =

Explanation:

Step1: Find the first term (\(a_1\))

For an arithmetic sequence \( \{a_n\} = \{7n + 8\} \), to find \( a_1 \), we substitute \( n = 1 \) into the formula.
\( a_1 = 7(1) + 8 = 7 + 8 = 15 \)

Step2: Find the second term (\(a_2\))

Substitute \( n = 2 \) into the formula \( a_n = 7n + 8 \).
\( a_2 = 7(2) + 8 = 14 + 8 = 22 \)

Step3: Find the third term (\(a_3\))

Substitute \( n = 3 \) into the formula \( a_n = 7n + 8 \).
\( a_3 = 7(3) + 8 = 21 + 8 = 29 \)

Step4: Find the fourth term (\(a_4\))

Substitute \( n = 4 \) into the formula \( a_n = 7n + 8 \).
\( a_4 = 7(4) + 8 = 28 + 8 = 36 \)

Step5: Find the common difference (\(d\))

The common difference \( d \) of an arithmetic sequence is \( a_{n + 1}-a_n \). Let's use \( a_2 - a_1 \).
\( d = a_2 - a_1 = 22 - 15 = 7 \)
We can also verify with \( a_3 - a_2 = 29 - 22 = 7 \) and \( a_4 - a_3 = 36 - 29 = 7 \), so the common difference is consistent.

Answer:

The common difference \( d = 7 \)
\( a_1 = 15 \)
\( a_2 = 22 \)
\( a_3 = 29 \)
\( a_4 = 36 \)