#### A sequence x_1, x_2, x_3......... is defined by x_1 = k , x_{n+1} = ax_n - 3 n 1,

Given that x_3 = 7, x_2\ =\ a\ -3

Find the possible values of a.

Anonymous

0

Given that x_3 = 7, x_2\ =\ a\ -3

Find the possible values of a.

Krishna

0

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 (calculate it otherwise they will mention in the question x_2 = a - 3)

x_ 3 = a(a - 3) - 3

x_3 = a^2 – 3a – 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 quadratic equation to find the requires value(a)

NOTE: Use the Factorization method

(Answer: a = 5 or – 2)