A sequence a_1, a_2, a_3 ... , is defined by a_1 = k, a_{n+1} = 3a_n + 5, n ≥ 1, where k is a positive integer. Show that a_3 = 9k + 20.

Step 1: Before going to do the problem, Find the known 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: To find the twenty-first term, replace n(any variable represents
position) 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_3
x_{n+1} = ax_n - 3
x_3 = ax_2 - 3
Substitute the values x_2(calculate\ it\ or\ given\ in\ the\ question\ x_2=a-3)
x_ 3 = a(a - 3) - 3
x_3 = a^2 - 3a - 3
Step 4: Simplify further
Step 5: Verify that the result and the given answer are same or not