City Guilds Model Questions Vol1 2023 Information Technology Question 28

Practice objective / multiple choice question 28 from the 2023 City Guilds Model Questions Vol1 Information Technology examination.

City Guilds Model Questions Vol1 2023 Information Technology Objective / Multiple Choice Hard Difficulty
Question 28 CITY_GUILDS_MODEL_QUESTIONS_VOL1 • 2023 • INFORMATION_TECHNOLOGY • objective

Consider the sequence defined by \(a_{1}=2\), \(a_{2}=3\) and for \(n\ge 3\), \(a_{n}=5a_{n-1}-6a_{n-2}\). (a) Derive a closed‑form expression for \(a_{n}\). (b) Using that expression, compute the value of \(a_{10}\).

Answer Options

A. Closed form: \(a_{n}=3\cdot2^{n}-3^{n-1}\); \(a_{10} = -14580\).
B. Closed form: \(a_{n}=3\cdot2^{n-1}+3^{n-1}\); \(a_{10} = 59049\).
Correct Answer C. Closed form: \(a_{n}=3\cdot2^{n-1}-3^{n-1}\); \(a_{10} = -18147\).
D. Closed form: \(a_{n}=2\cdot2^{n-1}-3^{n-1}\); \(a_{10} = -19683\).
Correct Answer
C
Correct Option:
Closed form: \(a_{n}=3\cdot2^{n-1}-3^{n-1}\); \(a_{10} = -18147\).

About This Question

This is City Guilds Model Questions Vol1 2023 Information Technology Question 28. It is one of the objective questions from the 2023 City Guilds Model Questions Vol1 Information Technology examination.

Difficulty level: Hard .

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