Math Problem Statement

Find the first three terms of the sequence defined by a_n = 10(2)^n, where n represents the position of a term in the sequence. Start with n = 1.

Solution

The given sequence is defined as:

an=10(2)na_n = 10(2)^n

We are asked to find the first three terms of the sequence starting with n=1n = 1.

Step-by-step calculation:

  1. For n=1n = 1: a1=10(2)1=10×2=20a_1 = 10(2)^1 = 10 \times 2 = 20

  2. For n=2n = 2: a2=10(2)2=10×4=40a_2 = 10(2)^2 = 10 \times 4 = 40

  3. For n=3n = 3: a3=10(2)3=10×8=80a_3 = 10(2)^3 = 10 \times 8 = 80

Final Answer:

The first three terms of the sequence are: 20,40,8020, 40, 80

Would you like further details or have any other questions? Here are some related questions you might explore:

  1. What is the 5th term of this sequence?
  2. How does the sequence grow as nn increases?
  3. Can this sequence be classified as arithmetic or geometric?
  4. What would happen to the sequence if the base were changed from 2 to another number?
  5. How could you express the nth term using logarithms?

Tip: Always check the behavior of a sequence for small values of nn to understand its growth or pattern.

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Math Problem Analysis

Mathematical Concepts

Sequences
Exponential Growth

Formulas

a_n = 10(2)^n

Theorems

None

Suitable Grade Level

Grades 7-9