Write as a Vector Equality a(31)=23 , d=5 , n=23

Problem

(a_31)=23,d=5,n=23

Solution

1. Identify the components of the arithmetic sequence formula in vector form.

2. Recall the general term formula for an arithmetic sequence, which is (a_n)=(a_1)+(n−1)*d

3. Substitute the given values (a_31)=23 d=5 and n=23 into the vector representation v=<(a_1),d,n>

4. Calculate the first term (a_1) using the formula 23=(a_1)+(31−1)*5

5. Solve for (a_1) to find (a_1)=23−150=−127

6. Express the relationship as a vector equality where the vector of parameters maps to the specific term value.

Final Answer

<(a_1),d,n>=<−127,5,23>

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