Question

what is the common difference between successive terms in the sequence?
2, 8, 14, 20, 26, ...

-6
-4
4
6

Explanation:

Step1: Recall common difference formula

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

Step2: Calculate difference between first two terms

Take \(a_1 = 2\) and \(a_2 = 8\). Then \(d=a_2 - a_1=8 - 2 = 6\).

Step3: Verify with other terms (optional but good)

Check \(a_3 - a_2=14 - 8 = 6\), \(a_4 - a_3=20 - 14 = 6\), \(a_5 - a_4=26 - 20 = 6\). So the common difference is 6.

Answer:

6 (corresponding to the option with 6)