9. What Is The 6th Term Of The Geometric Sequence 2/25, 2/5, 2, 10,2026?, A. 25 , B. 250 , C. 1250 , D. 2500

9. What is the 6th term of the geometric sequence 2/25, 2/5, 2, 10,…?

a. 25
b. 250
c. 1250
d. 2500

 

Geometric Sequence

The 6th term of the geometric sequence 2/25, 2/5, 2, 10,.... is 250.

Solution:

Geometric Sequence Formula: a_n = a₁r ⁿ ⁻ ¹

Given: a₁ = 2/25

          a₂ = 2/5

          a₃ = 2

          a₄ = 10

1. Find the common ratio.

       a_n = a₁r ⁿ ⁻ ¹

        a₂  = a₁r ⁿ ⁻ ¹

       2/5 = 2/25 r  ² ⁻ ¹

       2/5 = 2/25 r

2. Divide both sides of the equation by 2/25 to find r.

    2/5/2/25 = 2/25 r/2/25

  (2/5)(25/2) = r

          50/10 = r

                 5 = r

3. Using r = 5, find the 6th term of the geometric sequence.

            a_n = a₁r ⁿ ⁻ ¹

              a₆ = a₁r ⁿ ⁻ ¹

              a₆ = 2/25(5) ⁶ ⁻ ¹

              a₆ = 2/25 (5)⁵

              a₆ = 2/25 (3, 125)

              a₆ = 6, 250/25

             a₆ = 250

4. Therefore, the 6th term of the geometric sequence 2/25, 2/5, 2, 10….is 250.

Definition:

      A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Code: 10.3.1.1

For more information regarding geometric sequence , go to the following links:

brainly.ph/question/154960

brainly.ph/question/1461781

brainly.ph/question/1634458


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