Math Problem Statement

$3 $6 $9 $12 $15 $18 $21 $24 $27 $30 $33 $36 $39 $42 $45 $48 $51 $63 $66 $69 $72 $75 $78 $81 $54 $57 $60 $84 $87 $90 $93 $96 $99 $102 $105 $108 $111 $114 $117 $120 $123 $126 $129 $132 $135 $138 $141 $144 $147 $150 $153 $156 $159 $162 $165 $168 $171 $174 $177 $180 $183 $186 $189 $192 $195 $198 $201 $ 204$207 $210 $213 $216 $219 $222 $ 225$228$231 $234 $237 $240 $ 243$246 $ 249$252 $255 $258 $261 $ 264$267$270 $273 $ 276$279 $282 $285 $288 $291 $294 $297 $150

Solution

It seems like you've listed a sequence of numbers that is increasing by 3 each time, but there are some formatting inconsistencies (missing dollar signs, extra numbers like "204$207," and isolated numbers like "$150" at the end).

This looks like an arithmetic sequence, where the common difference between consecutive terms is 3. The sequence appears to start from 3 and continues in steps of 3. However, it seems that some values were entered incorrectly.

Let's first clarify the correct arithmetic sequence, assuming it was intended to be:

3,6,9,12,15,3, 6, 9, 12, 15, \ldots

This sequence increases by 3 each time, and if you want, I can calculate or analyze the next terms, find the sum of the first few terms, or solve for specific terms based on your needs.

Do you want me to fix or analyze this sequence in detail, such as finding the 100th term or the sum of the first N terms?


Related questions:

  1. How do you calculate the sum of an arithmetic sequence?
  2. What is the general formula for the nth term of an arithmetic sequence?
  3. Can you apply the same concept to a sequence with a different common difference?
  4. How do you determine if a given sequence is arithmetic?
  5. How can you solve for missing terms in an arithmetic sequence?

Tip:

When working with arithmetic sequences, always identify the first term (denoted as a1a_1) and the common difference (denoted as dd) to apply the formulas correctly.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Patterns and Series

Formulas

nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d
Sum of n terms: S_n = n/2 × (2a_1 + (n - 1)d)

Theorems

Arithmetic Sequence Formula

Suitable Grade Level

Grades 6-8