Question

What are the first four terms of an arithmetic sequence with these properties:

(a_1 = 2),
(a_n = a_n-1+ 5)?

A) 2, 7, 12, 17
B) 2, 5, 10, 15
C) 2, 5, 7, 12
D) 2, 7, 9, 14

Answer 1

The first four terms of the arithmetic sequence are 2, 7, 12, 17. These are obtained by starting with 2 and adding 5 to each subsequent term. Option A is correct.

Step-by-step explanation:

The question asks for the first four terms of an arithmetic sequence with the properties (a_1 = 2), (a_n = a_{n-1} + 5).

In an arithmetic sequence, each term after the first is obtained by adding a constant difference, in this case, 5, to the previous term.

Starting with the first term 2, we can determine the sequence by repeatedly adding 5:

• First term (a_1): 2
• Second term (a_2): 2 + 5 = 7
• Third term (a_3): 7 + 5 = 12
• Fourth term (a_4): 12 + 5 = 17

Therefore, the first four terms of the sequence are 2, 7, 12, 17. Option A is correct.