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What must be the the value of k so that 5k-3, k+2, and 3k-11 will form an arithmetic sequence?

Sagot :

Brainlymomshieidn

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:

  1. 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.

To learn more about arithmetic sequence, read the following links:

https://brainly.ph/question/629112

https://brainly.ph/question/634223

https://brainly.ph/question/370283

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