Question

17/30 determine the common difference (rate of change) for the arithmetic sequence -5, 12, 29, 46, ... 7 -7 -17 17

Explanation:

Step1: Recall common difference formula

For an arithmetic sequence, common difference \( d = a_{n + 1}-a_{n} \).

Step2: Calculate using first two terms

Take \( a_1=-5 \), \( a_2 = 12 \). Then \( d=a_2 - a_1=12-(-5)=12 + 5 = 17 \).

Step3: Verify with other terms

Check \( a_3 - a_2=29 - 12 = 17 \), \( a_4 - a_3=46 - 29 = 17 \). Consistent.

Answer:

17 (corresponding to the option with 17, e.g., if the last option is D. 17, then D. 17)