sequences - A sequence a_1, a_2, a_3........., is defined by, a_1 = k, a_{n+1} = 4a_n - 7, where k is a constant.

Krishna (last edited 3 years ago) (Expert, Educator @Qalaxia)

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 values(n). And simplify

EXAMPLE: x_n = 4n − 3

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 :

therefore x21 = 4 × 21 − 3 = 84 − 3 = 81

Step 4: Repeat the same steps to calculate a_3 in terms of k