Arithmetic Sequence Math Example 2

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Example 2

medium
In an arithmetic sequence a5=18a_5 = 18 and a12=46a_{12} = 46. Find a1a_1 and dd.

Solution

  1. 1
    Write: a1+4d=18a_1 + 4d = 18 and a1+11d=46a_1 + 11d = 46.
  2. 2
    Subtract: 7d=28⇒d=47d = 28 \Rightarrow d = 4.
  3. 3
    Back-substitute: a1=18−4(4)=2a_1 = 18 - 4(4) = 2.

Answer

a1=2a_1 = 2, d=4d = 4
Two equations, two unknowns. Subtracting eliminates a1a_1 to find dd first, then back-substitution gives a1a_1.

About Arithmetic Sequence

A sequence where each term is obtained from the previous by adding a fixed constant called the common difference dd.

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More Arithmetic Sequence Examples

Example 1 easy

An arithmetic sequence has [formula] and [formula]. Find [formula] and [formula].

Example 3 easy

Find the 15th term of [formula]

Example 4 medium

Find the sum of all integers from 1 to 100.

Example 5 medium

Find the sum of the first 20 terms of the arithmetic sequence: 5, 8, 11, 14, ...

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