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Find any of the values a_1, d, a_n, n, or S_n that are missing from the arithmetic sequence

5,12,19, …, 68
The value of a_1 is __

User Alan Kis
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1 Answer

7 votes

Final answer:

In an arithmetic sequence, the value of a_1 can be found by using the formula 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, and d is the common difference. By using the given information and solving for n, we find that a_1 is equal to 5.

Step-by-step explanation:

The given sequence is 5, 12, 19, ... , 68. To find the value of a_1, we need to determine the common difference, d.

The common difference is obtained by subtracting any two consecutive terms in the sequence.

Let's subtract 12 from 5: 12 - 5 = 7. Therefore, d = 7.

The formula to find the nth term of an arithmetic sequence is: a_n = a_1 + (n - 1) * d.

We can now substitute the given values to find a_n.

Let's use the last term, 68, to find n: 68 = a_1 + (n - 1) * 7. Since we know a_1 = 5 and d = 7, we can solve for n.

68 = 5 + (n - 1) * 7.

Simplifying the equation gives us: 68 = 5 + 7n - 7. Solving for n, we get n = 10.

Therefore, the value of a_1 is 5.

User Vell
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