#### A sequence is given by: x_1 = 1, x_{n+1} = x_n(p + x_n), where p is a constant (p ≠ 0).

Given that x_3 = 1

Find the value of p,

Write down the value of x_{2008}.

Anonymous

0

Given that x_3 = 1

Find the value of p,

Write down the value of x_{2008}.

Krishna

0

(i) Given that x_3 = 1

Find the value of p,

Step 1: Before going to do the problem, Find the knowns and unknowns in and note it down.

Step 2: Explore the given rule

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

Succeeding term = a (preceding term) - 3

Step 3: By using the given rule find the required term ( x_2, x_3,x_4...etc)

NOTE: According to the given rule substitute the values to get the required term.

EXAMPLE: For an attempt to find the x_3

x_{n+1} = ax_n - 3

x_3 = ax_2 - 3

Substitute the values x_2 (\text{Calculate it or given in the question }x_2 = a - 3)

x_ 3 = a(a - 3) - 3

Step 4: Equate the given term value to the term calculated by the rule (both represents the same value, so we can equate them)

EXAMPLE : a^2 – 3a – 3 = 7

Step 5: Simplify the equation to find the requires value(a)

(ii) Write down the value of x_{2008}

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 (n)values.

[NOTE: 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]

EXAMPLE: For an attempt to find the x_2 substitute n=1 in the given rule

x_{n+1} = ax_n - 3

x_2 = ax_1 - 3

Substitute the values x_1 [ take x_1 = 1 since n >1), Some times it mention

in the question]

x_ 2 = a(1) - 3

x_2 = a - 3

Step 4: Simplify further

(Apply the BODMAS rules)