Chapter8: Sequences, Series,and Probability
Section8.3: Geometric Sequences And Series
Problem 1ECP: Write the first four terms of the geometric sequence whose nth term is 6(2)n. Then find the common...
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![**Problem Statement:**
Find \( a_1 \) for the following arithmetic sequence.
Given:
- The sum of the first 12 terms, \( S_{12} = 120 \)
- The 12th term, \( a_{12} = 21 \)
**Objective:**
Calculate the first term of the sequence, \( a_1 \).
**Instructions:**
Use the formula for the sum of an arithmetic sequence:
\[
S_n = \frac{n}{2} (a_1 + a_n)
\]
Where:
- \( S_n \) is the sum of the first \( n \) terms
- \( a_1 \) is the first term
- \( a_n \) is the \( n \)th term
- \( n \) is the number of terms
Substitute the known values to solve for \( a_1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F228397b8-cd0e-4924-bc62-b0b7f3293021%2Ffb173b4c-2373-47bd-9587-71458bcdcd04%2Fhotnmy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \( a_1 \) for the following arithmetic sequence.
Given:
- The sum of the first 12 terms, \( S_{12} = 120 \)
- The 12th term, \( a_{12} = 21 \)
**Objective:**
Calculate the first term of the sequence, \( a_1 \).
**Instructions:**
Use the formula for the sum of an arithmetic sequence:
\[
S_n = \frac{n}{2} (a_1 + a_n)
\]
Where:
- \( S_n \) is the sum of the first \( n \) terms
- \( a_1 \) is the first term
- \( a_n \) is the \( n \)th term
- \( n \) is the number of terms
Substitute the known values to solve for \( a_1 \).
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