Finding a sum of an arithmetic sequence
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The document explains how to find the sum of the first 22 terms of the arithmetic sequence -4, -1, 2, 5, 8, where the common difference is 3. It provides the explicit formula for the nth term and calculates the 22nd term as 59. The final sum of the first 22 terms is determined to be 605.
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Finding a sum of an arithmetic sequence
- 1. Find the sum of the first 22 terms in the sequence below: -4, -1, 2, 5, 8, ….
- 2. Find the sum of the first 22 terms in the sequence: -4, -1, 2, 5, 8, …. • First, figure out if the sequence is arithmetic or geometric. • It is arithmetic because you are ADDING 3 each time.
- 3. Find the sum of the first 22 terms in the sequence: -4, -1, 2, 5, 8, …. • Next, write the explicit formula for this sequence. • 𝑎 𝑛 = 𝑎1 + 𝑛 − 1 𝑑 •Since the first term is -4, that is plugged in for a1. •The common difference is 3 •The new equation is: 𝑎 𝑛 = −4 + 𝑛 − 1 3
- 4. Find the sum of the first 22 terms in the sequence: -4, -1, 2, 5, 8, …. • Use your explicit formula to find the 22nd term. • 𝑎 𝑛 = −4 + 𝑛 − 1 3 • 𝑎22 = −4 + 22 − 1 3 = 59 •The value of the 22nd term is 59.
- 5. Find the sum of the first 22 terms in the sequence: -4, -1, 2, 5, 8, …. • Now find the sum! • 𝑆 𝑛 = 𝑛 2 𝑎1 + 𝑎 𝑛 where n is the number of terms, a1 is the first term and an is the last term • 𝑆22 = 22 2 −4 + 59 = 605 • The sum of the first 22 terms in this sequence will be 605.