Math Problem Statement

given the sequence form form 2,11,20,29,38.... What are the values of a1 and d?

Solution

The given sequence is: 2, 11, 20, 29, 38, ...

This is an arithmetic sequence, where each term increases by a constant difference.

  1. The first term (a1a_1) is the first number in the sequence: a1=2a_1 = 2

  2. The common difference (dd) is the difference between consecutive terms: d=112=9d = 11 - 2 = 9

Thus:

  • a1=2a_1 = 2
  • d=9d = 9

Would you like more details on how arithmetic sequences work, or do you have any questions?

Related questions:

  1. How can we find the nth term of an arithmetic sequence?
  2. How can we calculate the sum of the first n terms of this sequence?
  3. What is the difference between arithmetic and geometric sequences?
  4. How can we determine if a sequence is arithmetic just by looking at it?
  5. Can an arithmetic sequence have a negative common difference?

Tip: In arithmetic sequences, the common difference stays constant throughout the sequence!

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Series

Formulas

First term of an arithmetic sequence: a1 = a
Common difference: d = a(n) - a(n-1)

Theorems

Arithmetic sequence formula: a(n) = a1 + (n-1) * d

Suitable Grade Level

Grades 7-9