Algebraic Reasoning Question

Question

For the arithmetic sequence below determine the common difference and write the explicit rule and zero term

1. 128,96,64,32 (common difference= -32)
2. what is the zero term for the sequence?
3. what is the explicit rule for this sequence?

Answer 1

If by "zero term" you mean which term is zero, then

0 = 128 - (n - 1)(32)

0 = 128 - (32n - 32)

0 = 128 - 32n + 32

0 = 160 - 32n

32n = 160

n = 5

Or

128, 96, 64, 32, 0

Answer 2

The zeroth term in the sequence is the first term in the sequence....128.

The explicit rule of the sequence is developed by the pattern in the sequence.... so if the pattern is decreasing by 32. Then the explicit rule of the sequence {a_n} given is.... a_n+1 = a_n - 32.