Question

find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...
63, 72, 81
61, 70, 79
79, 88, 97
70, 79, 88

Explanation:

Step1: Find the common difference

In an arithmetic sequence, the common difference \(d\) is found by subtracting consecutive terms. Let's take the first two terms: \(34 - 25 = 9\), then \(43 - 34 = 9\), and \(52 - 43 = 9\). So the common difference \(d = 9\).

Step2: Find the next term after 52

To find the next term, we add the common difference to the last given term. So, \(52 + 9 = 61\)? Wait, no, wait. Wait, 52 + 9 is 61? Wait, no, let's check the options. Wait, maybe I made a mistake. Wait, 25, 34 (25+9), 43 (34+9), 52 (43+9), so next term is 52 + 9 = 61? But the options have 61,70,79? Wait, no, wait the options: first option is 63,72,81; second is 61,70,79; third is 79,88,97; fourth is 70,79,88. Wait, maybe my calculation is wrong. Wait, 25 to 34 is +9, 34 to 43 is +9, 43 to 52 is +9. So 52 + 9 = 61 (term 5), 61 + 9 = 70 (term 6), 70 + 9 = 79 (term 7). So the next three terms are 61, 70, 79.

Answer:

B. 61, 70, 79