Math Problem Statement

Given the nth term formula, complete the first five terms of the sequence an = 5n2 -2n for n ≥ 1

Solution

To find the first five terms of the sequence given by the formula an=5n22na_n = 5n^2 - 2n for n1n \geq 1, we substitute n=1,2,3,4,and5n = 1, 2, 3, 4, \text{and} 5 into the formula:

  1. For n=1n = 1: a1=5(1)22(1)=52=3a_1 = 5(1)^2 - 2(1) = 5 - 2 = 3

  2. For n=2n = 2: a2=5(2)22(2)=544=204=16a_2 = 5(2)^2 - 2(2) = 5 \cdot 4 - 4 = 20 - 4 = 16

  3. For n=3n = 3: a3=5(3)22(3)=596=456=39a_3 = 5(3)^2 - 2(3) = 5 \cdot 9 - 6 = 45 - 6 = 39

  4. For n=4n = 4: a4=5(4)22(4)=5168=808=72a_4 = 5(4)^2 - 2(4) = 5 \cdot 16 - 8 = 80 - 8 = 72

  5. For n=5n = 5: a5=5(5)22(5)=52510=12510=115a_5 = 5(5)^2 - 2(5) = 5 \cdot 25 - 10 = 125 - 10 = 115

Therefore, the first five terms of the sequence are 3,16,39,72,and1153, 16, 39, 72, \text{and} 115.

Would you like further details or have any questions?

Here are 5 numbered questions for you to ask:

  1. How do you derive the nth term formula for an arithmetic sequence?
  2. Can you explain how to find the derivative of a function?
  3. How do you solve systems of linear equations using matrix methods?
  4. What are the properties of logarithmic functions?
  5. Can you show me how to integrate a given function?

Tip: When working with sequences, always verify your calculations by substituting values back into the formula to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Sequences
Quadratic Equations

Formulas

nth term formula for sequences

Theorems

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Suitable Grade Level

Grades 7-9