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Find the indicated term of the arithmetic sequence.

31st term: 2.19, 2.34, 2.49, ...
The 31st term of the arithmetic sequence is ______.
A) 2.19
B) 2.34
C) 2.49
D) 2.64

1 Answer

2 votes

Final answer:

To find the 31st term of an arithmetic sequence, we can use the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. Substituting the given values, we find that the 31st term is 6.69.

Step-by-step explanation:

The arithmetic sequence is formed by adding a common difference to each term to get the next term. In this case, we need to find the 31st term of the sequence 2.19, 2.34, 2.49, ...

To find the 31st term, we can use the formula:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

Given that a1 = 2.19 and d = 0.15 (since the common difference is 2.34 - 2.19 = 0.15), we can substitute these values into the formula:

a31 = 2.19 + (31 - 1) * 0.15

Simplifying the expression:

a31 = 2.19 + 30 * 0.15

a31 = 2.19 + 4.5

a31 = 6.69

Therefore, the 31st term of the arithmetic sequence is 6.69. The correct answer is not listed in the options provided, so it would need to be added as an option E) None of the above.

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