Math Problem Statement
Write the following series in sigma notation. 2, plus, 11, plus, 20, plus, 29, plus, 38, plus, 47, plus, 56 2+11+20+29+38+47+56\
Solution
The given series is:
This is an arithmetic sequence where the first term and the common difference .
In general, the -th term of an arithmetic sequence is given by:
For this sequence:
The series can be written in sigma notation as:
This represents the sum of the first 7 terms of the arithmetic sequence.
Would you like more details or have any questions about this?
Here are 5 related questions:
- How do you find the common difference in an arithmetic sequence?
- What is the formula for the sum of an arithmetic series?
- How do you calculate the sum of an infinite arithmetic sequence?
- Can you convert this sigma notation into a closed-form expression?
- How do arithmetic sequences differ from geometric sequences?
Tip: In an arithmetic sequence, the common difference is constant between consecutive terms!
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Series
Sigma Notation
Formulas
General formula for arithmetic sequence: a_n = a + (n - 1)d
Sigma notation for arithmetic series: ∑_{n=1}^{N}(a_n)
Theorems
Arithmetic Sequence Formula
Suitable Grade Level
Grades 9-10
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