OCR
Further Additional Pure AS
2019
June
— Question 2
Exam Board
OCR
Module
Further Additional Pure AS (Further Additional Pure AS)
Year
2019
Session
June
Topic
Sequences and Series
2
The convergent sequence \(\left\{ \mathrm { a } _ { \mathrm { n } } \right\}\) is defined by \(a _ { 0 } = 1\) and \(\mathrm { a } _ { \mathrm { n } + 1 } = \sqrt { \mathrm { a } _ { \mathrm { n } } } + \frac { 4 } { \sqrt { \mathrm { a } _ { \mathrm { n } } } }\) for \(n \geqslant 0\). Calculate the limit of the sequence.
The convergent sequence \(\left\{ \mathrm { b } _ { \mathrm { n } } \right\}\) is defined by \(\mathrm { b } _ { 0 } = 1\) and \(\mathrm { b } _ { \mathrm { n } + 1 } = \sqrt { \mathrm { b } _ { \mathrm { n } } } + \frac { \mathrm { k } } { \sqrt { \mathrm { b } _ { \mathrm { n } } } }\) for \(n \geqslant 0\), where \(k\) is a constant.
Determine the value of \(k\) for which the limit of the sequence is 9 .