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Sequences and seriesAlgebraCollegeabout 0:33

Evaluate the sum of 3^k from k=1 to 6: animated lesson

A narrated, step-by-step sequences and series video lesson with captions. Final answer: 1092.

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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
$\sum_{k=1}^{6} {3}^{ k}$
2. Step by step
1. $\sum_{k=1}^{6} {3}^{ k}$
  Write the sum
2. $3 + 9 + 27 + \cdots$
  List the first terms
3. $\sum_{k=1}^{6} {3}^{ k} = 1092$
  Add all 6 terms exactly (as fractions)
3. The answer
$\text{1092}$
Σ = 1092
4. Check
- Decimal value: 1092

Transcript

The problem. Here is the problem: sum of 3 to the power k from k equals 1 to 6. Add the terms 3 ^ k for k equals 1, 2, …, 6 (6 terms).

Step by step. Write the sum. List the first terms. Add all 6 terms exactly (as fractions).

The answer. So the answer is 1092. Each term is computed exactly and added. For long arithmetic or geometric sums a closed formula gives the same result.

Check. Decimal value: 1092.

About sequences and series

Evaluate finite sums and arithmetic and geometric series.

Evaluate the sum of 3^k from k=1 to 6: Step-by-Step Lesson