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What is the next term of the geometric sequence? (4)/(9),-(4)/(3),4", "

What is the next term of the geometric sequence? \newline49\frac{4}{9}, −43-\frac{4}{3}, 44,

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Full solution

Q. What is the next term of the geometric sequence? \newline49\frac{4}{9}, −43-\frac{4}{3}, 44,
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic.\newlineIn the given sequence, each term is obtained by multiplying the previous term by a common ratio.\newlineThe given sequence is geometric.
  2. Find Common Ratio: Identify the common ratio of the sequence.\newlineTo find the common ratio, divide the second term by the first term.\newlineCommon Ratio rr = −43÷49-\frac{4}{3} \div \frac{4}{9} = −43×94-\frac{4}{3} \times \frac{9}{4} = −3-3
  3. Calculate Next Term: Find the next term in the sequence using the common ratio.\newlineThe third term is 44, so to find the fourth term, multiply the third term by the common ratio.\newlineNext Term = 4×(−3)=−124 \times (-3) = -12
  4. Check Pattern Consistency: Check the sequence to ensure that the next term follows the pattern.\newline(49)⋅(−3)=−(43)(\frac{4}{9}) \cdot (-3) = -(\frac{4}{3})\newline−(43)⋅(−3)=4-(\frac{4}{3}) \cdot (-3) = 4\newline4⋅(−3)=−124 \cdot (-3) = -12\newlineThe pattern is consistent, and the next term is correctly calculated.

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