Math Problem Statement

Tentukan beda pada barisan aritmetika di bawah ini!

Solution

The problem asks to find the "beda" (difference) for each arithmetic sequence provided. Let's go through each sequence one by one to determine the common difference.

a. 3,5,7,9,3, 5, 7, 9, \dots

  • The common difference dd is 53=25 - 3 = 2.

b. 4,104,204,4, 104, 204, \dots

  • The common difference dd is 1044=100104 - 4 = 100.

c. 5,3,1,1,5, 3, 1, -1, \dots

  • The common difference dd is 35=23 - 5 = -2.

d. 10,5,0,5,-10, -5, 0, 5, \dots

  • The common difference dd is 5(10)=5-5 - (-10) = 5.

e. 4,2,8,14,4, -2, -8, -14, \dots

  • The common difference dd is 24=6-2 - 4 = -6.

f. 30,24,18,12,-30, -24, -18, -12, \dots

  • The common difference dd is 24(30)=6-24 - (-30) = 6.

Thus, the common differences for each sequence are:

  • a: d=2d = 2
  • b: d=100d = 100
  • c: d=2d = -2
  • d: d=5d = 5
  • e: d=6d = -6
  • f: d=6d = 6

Would you like more details or have any questions on this?

Here are 5 questions to explore the topic further:

  1. What is the general formula for the nth term of an arithmetic sequence?
  2. Can you determine the 10th term of sequence a)?
  3. How do arithmetic sequences differ from geometric sequences?
  4. What would happen to the sequence if the common difference is 0?
  5. How would you approach finding the sum of the first nn terms of an arithmetic sequence?

Tip: When working with arithmetic sequences, always check if the difference between consecutive terms is constant to confirm it's arithmetic.

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Math Problem Analysis

Mathematical Concepts

Arithmetic sequences
Common difference

Formulas

d = a(n+1) - an

Theorems

Properties of arithmetic sequences

Suitable Grade Level

Grades 6-8