Question

find the common difference of the arithmetic sequence 10, 3, -4, …

Explanation:

Step1: Recall the formula for common difference

The common difference \( d \) of an arithmetic sequence is given by \( d = a_{n + 1}-a_{n} \), where \( a_{n+1} \) is the next term and \( a_{n} \) is the current term.

Step2: Calculate the common difference

Take the first two terms \( a_1 = 10 \) and \( a_2 = 3 \). Then \( d=a_{2}-a_{1}=3 - 10=- 7 \). We can verify with the next pair: \( a_3=-4 \), \( a_3 - a_2=-4 - 3=-7 \), which is consistent.

Answer:

\(-7\)