Q 18. The fifth term of an arithmetic sequence is 11 , and the tenth term is 41 . What is the FIRST term?

Ask by Kirk Rodriquez. in the United States

Jan 20,2025

Question

Q 18. The fifth term of an arithmetic sequence is 11 , and the tenth term is 41 . What is the FIRST term? $$ a_{1}=6 $$ $$ a_{1}=9 $$ $$ a_{1}=-13 $$ $$ a_{1}=-19 $$

UpStudy AI · Accepted Answer

To determine the first term $$ a_1 $$ of the arithmetic sequence, we'll use the information provided:

1. **Given:**
   - The 5th term $$ a_5 = 11 $$
   - The 10th term $$ a_{10} = 41 $$

2. **Arithmetic Sequence Formula:**
   $$
   a_n = a_1 + (n-1)d
   $$
   Where:
   - $$ a_n $$ is the $$ n $$-th term
   - $$ a_1 $$ is the first term
   - $$ d $$ is the common difference

3. **Set Up the Equations:**
   - For the 5th term:
     $$
     a_5 = a_1 + 4d = 11 \quad \text{(Equation 1)}
     $$
   - For the 10th term:
     $$
     a_{10} = a_1 + 9d = 41 \quad \text{(Equation 2)}
     $$

4. **Subtract Equation 1 from Equation 2:**
   $$
   (a_1 + 9d) - (a_1 + 4d) = 41 - 11
   $$
   $$
   5d = 30 \implies d = 6
   $$

5. **Find $$ a_1 $$ Using Equation 1:**
   $$
   a_1 + 4(6) = 11
   $$
   $$
   a_1 + 24 = 11
   $$
   $$
   a_1 = 11 - 24 = -13
   $$

**Answer:** $$ a_{1} = -13 $$
The first term $$ a_1 $$ is -13.

Q 18. The fifth term of an arithmetic sequence is 11 , and the tenth term is 41 . What is the FIRST term?

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