#### A sequence a_1, a_2, a_3......... is defined by a_1 = k , a_{n+1} = 2a_n - 7 n ≥ 1,

Show that a_3 = 4k – 21

Anonymous

1

Show that a_3 = 4k – 21

Krishna

1

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 terms (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 x_2 (x_2 = a - 3, take x_1 = 1 since n>1)]

x_ 3 = a(a - 3) - 3

x_3 = a^2 – 3a – 3

Step 4: Compare the result with the given answer, verify is it equating or not