Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it. 1.6 , 0.8 , 0 , − 0.8 , …
Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it. 1.6 , 0.8 , 0 , − 0.8 , …
Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive and an explicit formula to represent it.
1.6
,
0.8
,
0
,
−
0.8
,
…
Expert Solution & Answer
To determine
To find:Whether the given series is arithmetic or not and write the formula to represent it.
Answer to Problem 32P
The given sequence is arithmetic and the formula is A(n)=1.6+(n−1)(−0.8)
Explanation of Solution
Given:
The given series is 1.6,0.8,0,−0.8...
Calculation:
Calculate the common difference.
0.8−1.6=−0.80−0.8=−0.8−0.8−0=−0.8
Thus, the common difference it -0.8 so, the sequence is arithmetic.
Write the formula to represent the equation.
A(n)=A(1)+(n−1)d
Substitute the values in the above equation.
A(n)=1.6+(n−1)(−0.8)
Thus, the given sequence is arithmetic and the formula is A(n)=1.6+(n−1)(−0.8)
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