Find the indicated terms of the arithmetic sequence with the given description.The 50th term is 950, and the common difference is 5. Find the first and second terms.
Question
Find the indicated terms of the arithmetic sequence with the given description.The 50th term is 950, and the common difference is 5. Find the first and second terms.
Solution
To find the first term of an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence, which is a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term in the sequence, and d is the common difference.
Given that the 50th term (a_50) is 950 and the common difference (d) is 5, we can substitute these values into the formula:
950 = a_1 + (50 - 1) * 5 950 = a_1 + 49 * 5 950 = a_1 + 245
To find the first term (a_1), we can subtract 245 from both sides of the equation:
950 - 245 = a_1 705 = a_1
So, the first term of the sequence is 705.
To find the second term, we can add the common difference to the first term:
a_2 = a_1 + d a_2 = 705 + 5 a_2 = 710
So, the second term of the sequence is 710.
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