Question

A sequence has t(3)=18 and a common difference of 5. List the first 5 terms in the sequence

A. 5, 8, 11, 14, 17
B. 18, 23, 28, 33, 38
C. 8, 13, 18, 23, 28
D. 28, 23, 18, 13, 8​

Answer 1

The first 5 terms of the arithmetic sequence with a common difference of 5 and t(3) = 18 are 8, 13, 18, 23, 28.

Therefore, the correct answer is option C

Step-by-step explanation:

The formula to find the n-th term of an arithmetic sequence is tn = t1 + (n-1)d, where tn represents the n-th term, t1 is the first term, and d is the common difference. In this case, t3 is given as 18 and the common difference is 5.

Substituting these values into the formula, we can solve for t1:

18 = t1 + (3-1)(5)

18 = t1 + 2(5)

18 = t1 + 10

t1 = 18 - 10 = 8

Now we can list the first 5 terms of the sequence starting from t1 with a common difference of 5:

8, 8 + 5 = 13, 13 + 5 = 18, 18 + 5 = 23, 23 + 5 = 28

Therefore, the correct answer is option C. 8, 13, 18, 23, 28.