Question

Find the fourth term of the given sequence given a1

Answer 1

a4 = -10

Explanation:

Our givens are:

`a_1 = 10\\a_n = (-1)^n \cdot a_(n - 1) + 5`

Since we do not know the value of a3 to substitute as
`a_(n - 1)` to find a4, we'll find the terms prior to the fourth term by substituting their respective indices into the given formula, starting with n = 2 and incrementing by 1 each time.

`a_1 = 10\\a_2 = (-1)^2 \cdot a_(2 - 1) + 5 = 1 \cdot a_1 + 5 = 10 + 5 = 15\\a_3 = (-1)^3 \cdot a_(3 - 1) + 5 = -1 \cdot a_2 + 5 = -15 + 5 = -10\\a_4 = (-1)^4 \cdot a_(4 - 1) + 5 = 1 \cdot a_3 + 5 = -10 + 5 = -5`

Therefore, a4 = -10.