d. How many terms does the finite sequence 7, 16, 25, 34, 43, . . ., 1231 have? e. Find the sum: 7 + 16 + 25 +34 +43 + +1231 f. Use what you found above to find bn, the nth term of 4, 11, 27, 52, 86, . . . where bo = 4. bn
d. How many terms does the finite sequence 7, 16, 25, 34, 43, . . ., 1231 have? e. Find the sum: 7 + 16 + 25 +34 +43 + +1231 f. Use what you found above to find bn, the nth term of 4, 11, 27, 52, 86, . . . where bo = 4. bn
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Consider the sequence \(7, 16, 25, 34, 43, \ldots\) with \(a_1 = 7\).**
a. **Which of the following is a recursive definition for the sequence? Select all that apply.**
- \( \square \) A. \( a_n = 9 \cdot a_{n-1}; \, a_1 = 7 \)
- \( \square \) B. \( a_n = 7 \cdot 9^n \)
- \( \square \) C. \( a_n = a_{n-1} + a_{n-2}; \, a_1 = 7 \)
- \( \checkmark \) D. \( a_n = a_{n-1} + 9; \, a_1 = 7 \)
b. **Give a closed formula for the \(n\)th term of the sequence.**
\[ a_n = \boxed{9n - 2} \]
c. **Is 4552 a term in the sequence?**
- \( \circ \) A. No, it is larger than 1231
- \( \circ \) B. Yes, it is \( a_{4552} \)
- \( \circ \) C. No, it is between 4550 and 4559
- \( \circ \) D. Yes, it is \( a_{505} \)
- \( \checkmark \) E. Yes, it is \( a_{506} \)
d. **How many terms does the finite sequence \(7, 16, 25, 34, 43, \ldots, 1231\) have?**
\[ \boxed{} \]
e. **Find the sum: \(7 + 16 + 25 + 34 + 43 + \ldots + 1231\)**
\[ \boxed{} \]
f. **Use what you found above to find \(b_n\), the \(n\)th term of \(4, 11, 27, 52, 86, \ldots\) where \(b_0 = 4\).**
\[ b_n = \boxed{} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff37d99-6df7-4773-b15e-140cb7fb42c8%2Fd672c854-9fc6-4c62-8f0b-881ce3eb0230%2Fcgiix0e_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the sequence \(7, 16, 25, 34, 43, \ldots\) with \(a_1 = 7\).**
a. **Which of the following is a recursive definition for the sequence? Select all that apply.**
- \( \square \) A. \( a_n = 9 \cdot a_{n-1}; \, a_1 = 7 \)
- \( \square \) B. \( a_n = 7 \cdot 9^n \)
- \( \square \) C. \( a_n = a_{n-1} + a_{n-2}; \, a_1 = 7 \)
- \( \checkmark \) D. \( a_n = a_{n-1} + 9; \, a_1 = 7 \)
b. **Give a closed formula for the \(n\)th term of the sequence.**
\[ a_n = \boxed{9n - 2} \]
c. **Is 4552 a term in the sequence?**
- \( \circ \) A. No, it is larger than 1231
- \( \circ \) B. Yes, it is \( a_{4552} \)
- \( \circ \) C. No, it is between 4550 and 4559
- \( \circ \) D. Yes, it is \( a_{505} \)
- \( \checkmark \) E. Yes, it is \( a_{506} \)
d. **How many terms does the finite sequence \(7, 16, 25, 34, 43, \ldots, 1231\) have?**
\[ \boxed{} \]
e. **Find the sum: \(7 + 16 + 25 + 34 + 43 + \ldots + 1231\)**
\[ \boxed{} \]
f. **Use what you found above to find \(b_n\), the \(n\)th term of \(4, 11, 27, 52, 86, \ldots\) where \(b_0 = 4\).**
\[ b_n = \boxed{} \]
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