What kind of sequence is this? 216, 201, 186, 171, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Pattern Analysis: To determine the type of sequence, we need to look at the pattern of the numbers. Let's check the difference between consecutive terms. Calculation: 201 - 216 = -15 186 - 201 = -15 171 - 186 = -15Constant Difference: Since the difference between consecutive terms is constant, this indicates that the sequence is an arithmetic sequence.Arithmetic Sequence Definition: An arithmetic sequence is defined by having a constant difference between terms, which we have established is -15 in this case. This does not fit the definition of a geometric sequence, which requires each term to be obtained by multiplying the previous term by a constant factor.Sequence Type Determination: Therefore, the sequence is arithmetic, and the correct choice is (A) arithmetic.

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What kind of sequence is this? $\newline$ $216, 201, 186, 171, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Math Problems

Grade 8

Identify arithmetic and geometric sequences

Full solution

Q. What kind of sequence is this?

\newline

216, 201, 186, 171, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Pattern Analysis: To determine the type of sequence, we need to look at the pattern of the numbers. Let's check the difference between consecutive terms. $\newline$ Calculation: $\newline$ $201 - 216 = -15$ $\newline$ $186 - 201 = -15$ $\newline$ $171 - 186 = -15$
Constant Difference: Since the difference between consecutive terms is constant, this indicates that the sequence is an arithmetic sequence.
Arithmetic Sequence Definition: An arithmetic sequence is defined by having a constant difference between terms, which we have established is $-15$ in this case. This does not fit the definition of a geometric sequence, which requires each term to be obtained by multiplying the previous term by a constant factor.
Sequence Type Determination: Therefore, the sequence is arithmetic, and the correct choice is $(A)$ arithmetic.