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Determine the 84th term of the arithmetic sequence 18, 31, 44, ...?

A. 243
B. 246
C. 249
D. 252

User OJ Kwon
by
8.1k points

1 Answer

6 votes

Final Answer:

The 84th term of the arithmetic sequence is 1097.

Step-by-step explanation:

1. Finding the common difference:

We can find the common difference of the arithmetic sequence by subtracting the first term from the second term:

31 - 18 = 13

Therefore, the common difference is 13.

2. Finding the 84th term:

To find the 84th term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1) * d

where:

a_n is the nth term

a_1 is the first term

n is the number of terms

d is the common difference

In this case:

a_1 = 18 (first term)

n = 84 (number of terms)

d = 13 (common difference)

Substituting these values into the formula, we get:

a_84 = 18 + (84 - 1) * 13

a_84 = 18 + 1079

a_84 = 1097

Therefore, the 84th term of the arithmetic sequence is 1097.

User Kiseok
by
9.2k points
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