How to Solve an Arithmetic Sequence problem with Variable Terms

Save

This Article will show How to solve an Arithmetic Sequence Problem whose terms are variable terms. We will use an Example Problem to demonstrate how this is done.

Things You'll Need

  • Paper and
  • Pencil.
  • Given the following Arithmetic Sequence Problem. For some real number t, the first three terms of an arithmetic sequence are 2t, 5t-1, and 6t+2.
    What is the numerical value of the fourth term?
    We will explain in the following Steps how we solve this problem.

  • What Defines an Arithmetic Sequence is the common Difference between each term of the Arithmetic Sequence, that is the Difference between the Second term and the First term, should be the same or equal to the Difference between the Third term and the Second term, should be equal to the Difference between the Fourth term and the Third term, and so on.

  • In the problem given in Step #1, 2t, is the First term of the Arithmetic Sequence, 5t-1, is the Second term of the Sequence, and 6t+2, is the Third term of the Arithmetic Sequence. So since we are working with an Arithmetic Sequence, then (5t-1) - 2t should equal (6t+2) - (5t-1). that is we have an equation:
    (5t-1)-2t = (6t+2)-(5t-1),which is equivalent to 5t-2t-1 = 6t-5t+2+1.
    which is equivalent to, 3t-1 = t+3 that is 3t-t = 3+1. so 2t = 4 and t=2.

  • Since t=2, we should find the Fourth term of the Arithmetic Sequence in terms of t, then substitute t=2, for the t in that Fourth term.
    The Common Difference in our Arithmetic Sequence Problem, 2t, 5t-1, 6t+2,..., is 5t-1-2t = 3t-1. We now add 3t-1 to the Third term, 6t+2, and we get our Fourth term, 6t+2 + 3t-1 = 9t+1. by substituting t=2 in 9t+1, we get, 9(2)+1, which equals 18+1 = 19.

    So the numerical value of the Fourth term is ... 19.

Promoted By Zergnet

Comments

You May Also Like

  • How to Solve Math Problems

    Math problems can be very different depending on what type of math you are doing. People generally have the most difficulty with...

  • How to Find a Number of Terms in Arithmetic Sequence

    Equal intervals, called the common difference, separate the terms of an arithmetic sequence. The common difference can be either a positive or...

  • How to Find Fraction Sequences

    Algebra class will frequently require you to work with sequences, which can be arithmetic or geometric. Arithmetic sequences will involve obtaining a...

  • How to Solve Rational Numbers Sequence Problems

    Solving a rational numbers sequence always requires you to keep a few basic things in mind. Solve rational numbers sequences with help...

  • How to Solve a Math Pattern

    In order to solve a math pattern, a few numbers of the pattern need to be provided first. Learn about arithmetic and...

  • Solving Math Sequences

    There are two kinds of math sequences that can be solved: arithmetic sequences and geometric sequences. An arithmetic sequence is solved by...

  • Problem Solving in Mathematics

    To problem solve in mathematics, take each problem step-by-step, expand the problem for more clarity and be meticulous with each stage of...

Related Searches

Check It Out

Can You Take Advantage Of Student Loan Forgiveness?

M
Is DIY in your DNA? Become part of our maker community.
Submit Your Work!