Answer:
To find the sum of the first 20 terms of the given sequence, you can use the formula for the sum of an arithmetic series:
\[ S_n = \frac{n}{2}[2a + (n-1)d] \]
In this formula:
- \( S_n \) is the sum of the first \( n \) terms,
- \( n \) is the number of terms (in this case, 20),
- \( a \) is the first term of the sequence,
- \( d \) is the common difference between terms.
For the given sequence:
\[ a = 3 - (-1) = 4 \]
\[ d = \frac{4}{3 - (-1)} = \frac{4}{4} = 1 \]
Now, plug these values into the sum formula:
\[ S_{20} = \frac{20}{2}[2(4) + (20-1)(1)] \]
Calculate this expression to find the sum of the first 20 terms of the sequence.
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Answers & Comments
Answer:
To find the sum of the first 20 terms of the given sequence, you can use the formula for the sum of an arithmetic series:
\[ S_n = \frac{n}{2}[2a + (n-1)d] \]
In this formula:
- \( S_n \) is the sum of the first \( n \) terms,
- \( n \) is the number of terms (in this case, 20),
- \( a \) is the first term of the sequence,
- \( d \) is the common difference between terms.
For the given sequence:
\[ a = 3 - (-1) = 4 \]
\[ d = \frac{4}{3 - (-1)} = \frac{4}{4} = 1 \]
Now, plug these values into the sum formula:
\[ S_{20} = \frac{20}{2}[2(4) + (20-1)(1)] \]
Calculate this expression to find the sum of the first 20 terms of the sequence.