If the third term of an arithmetic sequence is 13 and the 9th term is 37, what is the 53rd term

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1. If the term of an arithmetic sequence is and the term is , what is the common difference? 2. What is the arithmetic mean between and ? 3. In an arithmetic sequence, and . Find the first term and the common difference. 4. The first three terms and the last term of a finite arithmetic sequence are , , ,..., . Find the number of terms in the sequence. 5. How many multiples are there between and ?

Instead of doing the problem for you, I'll do one exactly like yours, step by step: if the 4th term of an arithmetic sequence is 21 and the 11th term is 56, what is the common difference? __, __, __, 21, __, __, __, __, __, __, 56,...

when n=4, a4=21

when n=11, a11=56

So we have this system

Solve the first equation for a1

Substitute (21-3d) for a1 in

The common difference is 5. Now do yours the exact same way. It's not necessary, but if you like you can find the first term by substituting d=5 in

and find the arithmetic sequence to be: 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56,... Edwin

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If the third term of an arithmetic sequence is 13 and the 9th term is 37, what is the first term?

To find the first term, we need to use the arithmetic sequence formula:

» Substitute the given to the formula and make two equations.

» Now that we have made and equation, we have a problem. There are two unknown variables (the first term and the common difference). We could use the elimination method by subtracting the two equations.

» The common difference is 4. We could use this to substitute to either of the given equations and to find the first term.