Question

find the term a14 when a1 = 8 and d = ¼

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To find the term \(a_{14}\) in an arithmetic sequence where the first term \(a_1 = 8\) and the common difference \(d = \frac{1}{4}\), we use the formula for the \(n\)-th term of an arithmetic sequence, which is:

a_n = a_1 + (n-1)d

Therefore, to find the 14th term (\(a_{14}\)):

a_{14} = 8 + (14-1)\frac{1}{4}

a_{14} = 8 + 13 \cdot \frac{1}{4}

a_{14} = 8 + \frac{13}{4}

a_{14} = 8 + 3.25

a_{14} = 11.25

\[Solution\]

a_{14} = 11.25

\[Step-by-Step\]

1. Use the formula for the \(n\)-th term of an arithmetic sequence:

a_n = a_1 + (n-1)d

2. Plug in \(a_1 = 8\), \(d = \frac{1}{4}\), and \(n = 14\):

a_{14} = 8 + (14-1) \cdot \frac{1}{4}

3. Simplify the expression inside the parentheses:

a_{14} = 8 + 13 \cdot \frac{1}{4}

4. Multiply:

a_{14} = 8 + \frac{13}{4}

5. Convert the whole number to fraction and add:

a_{14} = \frac{32}{4} + \frac{13}{4} = \frac{45}{4}

6. Finally, convert back to a decimal:

a_{14} = 11.25

\[Solution\]

a_{14} = 11.25

Therefore, to find the 14th term (\(a_{14}\)):

\[Solution\]

\[Step-by-Step\]

1. Use the formula for the \(n\)-th term of an arithmetic sequence:

2. Plug in \(a_1 = 8\), \(d = \frac{1}{4}\), and \(n = 14\):

3. Simplify the expression inside the parentheses:

4. Multiply:

5. Convert the whole number to fraction and add:

6. Finally, convert back to a decimal:

\[Solution\]

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