#### A sequence is defined by the recurrence relation u_{n + 1} = \sqrt{(\frac{u_n}{2} + \frac{a}{u_n})} , n = 1, 2, 3, ..., where a is a constant.

Given instead that u_1 = u_2 = 3,

(i)Calculate the value of a,

(ii) write down the value of u_5.

Anonymous

0

Given instead that u_1 = u_2 = 3,

(i)Calculate the value of a,

(ii) write down the value of u_5.

Krishna

0

i) Calculate the value of a,

Step 1: Find the required term from the given rule.

NOTE: Substitute the suitable n value in the given rule to find the term

EXAMPLE: To find the a_3 term, replace n with the 2

a_{n+1} = 4a_n - 7

a_{2+1} = 4a_2 - 7 (since a_2=4k-7)

a_3 = 4(4k - 7) - 7

Step 2: Equate the term with the given value and simplify for the k(any varia) value

EXAMPLE: 4(4k-7) = 13

16k − 35 = 13

ii) write down the value of u_5

Step 1: Make sure that the given set of numbers arranged in some particular order. Because the question says that the set of numbers in sequence.

Step 2; Explore the given rule

EXAMPLE: x_{n+1} = ax_n - 3

Succeeding term = a (preceding term) - 3

Step 3: According to the given rule substitute the values(n). And simplify

EXAMPLE: x_n = 4n − 3

To find the twenty-first term, replace n by 21. based up on the rule it(n) may

change to lower value or higher value :

therefore x21 = 4 × 21 − 3 = 84 − 3 = 81

Step 4: Repeat the same steps to calculate some other terms in terms of k (any variable)