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Sequences and seriesAlgebraCollegeabout 0:25

Calculate 1 + 2 + 3 + ... + 50: animated lesson

A narrated, step-by-step sequences and series video lesson with captions. Final answer: 1275.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
1 + 2 + 3 + ... + 50
2. Step by step
1. $n = \frac{50 - 1}{1} + 1 = 50$
  Count the terms
2. $S = \frac{n(a_1 + a_n)}{2} = \frac{50(1 + 50)}{2} = 1275$
  Use the arithmetic series formula
3. The answer
$1275$
1275

Transcript

The problem. Here is the problem: 1 plus 2 plus 3 plus... plus 50. An arithmetic series: first term 1, common difference 1, last term 50.

Step by step. Count the terms. Use the arithmetic series formula.

The answer. So the answer is 1275. An arithmetic series: first term 1, common difference 1, last term 50.

About sequences and series

Evaluate finite sums and arithmetic and geometric series.

Calculate 1 + 2 + 3 + ... + 50: Animated Step-by-Step Lesson