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Example 3 Self Tutor Find

k

given that

3 k+1, k

, and -3 are consecutive ter...

Aug 21, 2024

Generated Graph

Solution by Steps

step 1

We know that for three terms to be consecutive in an arithmetic sequence, the middle term must be the average of the other two. Thus, we can set up the equation:

k = \frac{(3k + 1) + (-3)}{2}

step 2

Simplifying the equation gives us:

k = \frac{3k - 2}{2}

step 3

Multiplying both sides by 2 to eliminate the fraction results in:

2k = 3k - 2

step 4

Rearranging the equation leads to:

2 = 3k - 2k

k = -2

Answer

The value of

k

is -2

Key Concept

In an arithmetic sequence, the middle term is the average of the two outer terms.

Explanation

We derived the value of

k

by setting up an equation based on the property of arithmetic sequences and solving for

k