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. Write down an expression for a_2 in terms of k.

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(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_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)