Math Problem Statement

What is the 80th term in the sequence 3, 6, 9, 12,...?

Solution

The given sequence is 3,6,9,12,3, 6, 9, 12, \dots. This is an arithmetic sequence where the first term a1=3a_1 = 3 and the common difference d=3d = 3.

To find the nn-th term of an arithmetic sequence, the formula is:

an=a1+(n1)da_n = a_1 + (n-1) \cdot d

Substitute the values for a1=3a_1 = 3, d=3d = 3, and n=80n = 80:

a80=3+(801)3=3+793=3+237=240a_{80} = 3 + (80-1) \cdot 3 = 3 + 79 \cdot 3 = 3 + 237 = 240

Thus, the 80th term of the sequence is 240.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions you might explore:

  1. What is the sum of the first 80 terms of this sequence?
  2. What is the general formula for the sum of an arithmetic sequence?
  3. How would you find the 50th term in a sequence with a common difference of 5?
  4. If the sequence starts at 5 instead of 3, what would be the 80th term?
  5. What is the difference between an arithmetic sequence and a geometric sequence?

Tip: In an arithmetic sequence, the difference between consecutive terms is always constant.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Linear Algebra

Formulas

a_n = a_1 + (n-1) * d

Theorems

Arithmetic Sequence Formula

Suitable Grade Level

Grades 6-8