QuestionFind the 300th term of the sequence 57, 66, 75, 84, 93 using . Options: A. 2784 B. 2691 C. 2748 D. 2757
Studdy Solution
STEP 1
Assumptions1. The sequence is an arithmetic sequence, which is a sequence of numbers in which the difference between any two consecutive terms is constant. . The formula for the nth term of an arithmetic sequence is , where is the nth term, is the first term, is the term number, and is the common difference.
STEP 2
First, we need to find the common difference of the sequence. We do this by subtracting the first term from the second term.
STEP 3
Now, plug in the given values for the first and second terms to calculate the common difference.
STEP 4
Calculate the common difference.
STEP 5
Now that we have the common difference, we can find the300th term of the sequence using the formula .
STEP 6
Plug in the values for the first term, the common difference, and the term number to calculate the300th term.
STEP 7
implify the expression inside the parentheses.
STEP 8
Perform the multiplication.
STEP 9
Add the two numbers to find the300th term.
So, the300th term of the sequence is2748.
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