Arithmetic Sequence Math Example 4

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Example 4

medium
Find the sum of all integers from 1 to 100.

Solution

  1. 1
    Arithmetic sequence: a1=1a_1=1, a100=100a_{100}=100, n=100n=100.
  2. 2
    S100=1002(1+100)=50×101=5050S_{100} = \frac{100}{2}(1+100) = 50 \times 101 = 5050.

Answer

50505050
The sum formula pairs terms from opposite ends: 1+100=2+99=⋯=1011+100 = 2+99 = \cdots = 101. With 50 such pairs the total is 50×101=505050 \times 101 = 5050.

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 2 medium

In an arithmetic sequence [formula] and [formula]. Find [formula] and [formula].

Example 3 easy

Find the 15th term of [formula]

Example 5 medium

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

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