Arithmetic Sequence:
The value of k so that 5k-3, k+2, and 3k-11 will form an arithmetic sequence is 3. Since 5k – 3 when replaced by 3 is 5(3) – 3 = 15 – 3 = 12, then k + 2 when replaced by 3 is 3 + 2 = 5, and 3k – 11 when replaced by 3 is 3(3) – 11 = 9 – 11 = -2. Thus, the arithmetic sequence will be 12, 5, -2 where the common difference is 7.
Definition:
An arithmetic sequence is a sequence of numbers such that the difference of any two succeeding terms of the sequence is a constant while an arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, a and last term, an, divide by 2 in order to get the mean of the two values and then multiply by the number of values.
Step by Step Solution:
- Identify the given.
5k – 3 – 1st term of the arithmetic sequence
k + 2 – 2nd term of the arithmetic sequence
3k – 11 – 3rd term of the arithmetic sequence
2. Identify what is asked.
k = ?
3. Write the formula.
d = a_2 – a_1 or a_3 – a_2
4. Give the solution.
a_2 – a_1 = a_3 – a_2
(k + 2) – (5k – 3) = (3k – 11) – (k + 2)
k – 5k + 2 – (-3) = 3k – k – 11 – 2
-4k + 5 = 2k – 13
5. Simplify the equation.
-4k – 2k = -13 - 5
-6k = -18
6. Divide both sides of the equation by -6 to find the value of k.
-6k/-6 = -18/-6
Therefore, k = 3.
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