GED Mathematical Reasoning TestAlgebraic Problem Solving with Graphs and FunctionsEasy
A gardener is planting rows of flowers. The number of flowers he plants each day follows a pattern: 5, 8, 11, 14, ... . If this pattern continues, what is the total number of flowers he will have planted after 6 days?
- A20
- B75
- C17
- D69
Show answer & explanationAnswer & explanation
Correct answer: D. 69
This is an arithmetic sequence with a common difference of 3. The terms are a1=5, a2=8, a3=11, a4=14. The 5th term is 14+3=17, and the 6th term is 17+3=20. The total number of flowers after 6 days is the sum of the first 6 terms: 5 + 8 + 11 + 14 + 17 + 20 = 75.
Why the other options are wrong
- A. This is the 6th term in the sequence, not the total sum.
- B. Correct. The sum of the first 6 terms is 5 + 8 + 11 + 14 + 17 + 20 = 75.
- C. This is the 5th term in the sequence, not the total sum.
Arithmetic Sequence and Series
An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant (common difference). An arithmetic series is the sum of the terms of an arithmetic sequence.
- General term: an = a1 + (n-1)d, where a1 is the first term and d is the common difference.
- Sum of n terms: Sn = n/2 * (a1 + an) or Sn = n/2 * (2a1 + (n-1)d).
- To find the next term, add the common difference.
Memory trick: Add the first and last, multiply by half the count!