Each term in the sequence below is 2 ⁄ 3 times the previous term. What is the seventh term of the sequence?

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Accepted Answer

The fourth term in the sequence is 16 ⁄ 3 . You are looking for the seventh term, which is three terms after the fourth term. You must multiply by 2 ⁄ 3 three times, so the seventh term will be ( 2 ⁄ 3 ) 3 = 8 ⁄ 27 times 16 ⁄ 3 ; ( 8 ⁄ 27 )( 16 ⁄ 3 ) = 128 ⁄ 81 . Alternatively, every term in the sequence is 18 times 2 ⁄ 3 raised to a power. The first term, 18, is 18 × ( 2 ⁄ 3 ) 0 . The second term, 12, is 18 × ( 2 ⁄ 3 ) 1 . The value of the exponent is one less than the position of the term in the sequence. The seventh term of the sequence is equal to 18 × ( 2 ⁄ 3 ) 6 = 18 × ( 64 ⁄ 729 ) = 2 × ( 64 ⁄ 81 ) = 128 ⁄ 81 .

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