for each sequence, determine whether it appears to be arithmetic. if it does, find the common…

for each sequence, determine whether it appears to be arithmetic. if it does, find the common difference.\n4, 20, 100, 500, ...\narithmetic\ncommon difference: d = \nnot arithmetic\n9, 5, 1, - 3, ...\narithmetic\ncommon difference: d = \nnot arithmetic\n14, 17, 20, 23, ...\narithmetic\ncommon difference: d = \nnot arithmetic

for each sequence, determine whether it appears to be arithmetic. if it does, find the common difference.\n4, 20, 100, 500, ...\narithmetic\ncommon difference: d = \nnot arithmetic\n9, 5, 1, - 3, ...\narithmetic\ncommon difference: d = \nnot arithmetic\n14, 17, 20, 23, ...\narithmetic\ncommon difference: d = \nnot arithmetic

Answer

Explanation:

Step1: Check first sequence

Calculate differences between consecutive terms. $20 - 4=16$, $100 - 20 = 80$. Since $16\neq80$, it's not arithmetic.

Step2: Check second sequence

Calculate differences. $5 - 9=-4$, $1 - 5=-4$, $-3 - 1=-4$. It's arithmetic with common - difference $d=-4$.

Step3: Check third sequence

Calculate differences. $17 - 14 = 3$, $20 - 17 = 3$, $23 - 20 = 3$. It's arithmetic with common - difference $d = 3$.

Answer:

4, 20, 100, 500, ...: Not arithmetic 9, 5, 1, -3, ...: Arithmetic, $d=-4$ 14, 17, 20, 23, ...: Arithmetic, $d = 3$