Question
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Tutor-Verified Answer
Answer
\( a_{51} = 197 \)
Solution
To find \( a_{51} \) given the formula \( a_n = 4n - 7 \), we can substitute \( n = 51 \) into the formula.
\[
a_{51} = 4(51) - 7
\]
Calculating this step-by-step:
1. Calculate \( 4 \times 51 \):
\[
4 \times 51 = 204
\]
2. Subtract 7 from 204:
\[
204 - 7 = 197
\]
Thus, \( a_{51} = 197 \).
The final answer is:
\[
\boxed{197}
\]
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Simplify this solution Bonus Knowledge
To find \( a_{51} \), you can substitute \( n = 51 \) into the formula \( a_{n} = 4n - 7 \). So, \( a_{51} = 4(51) - 7 = 204 - 7 = 197 \). Thus, \( a_{51} = 197 \). This formula represents a linear sequence where each term is determined by multiplying the index by 4 and then subtracting 7. You can imagine this as a staircase rising steadily with each step as you go higher in the number of terms!
