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Type the missing number in this sequence:\newline6,  36,  216,  ____,  7,7766,\;36,\;216,\;\_\_\_\_,\;7,776

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Find terms of a geometric sequenceright chevron icon

Full solution

Q. Type the missing number in this sequence:\newline6,  36,  216,  ____,  7,7766,\;36,\;216,\;\_\_\_\_,\;7,776
  1. Identify Sequence Type: Is the given sequence geometric or arithmetic? Each term seems to be multiplied by a common ratio to obtain the next number. The given sequence appears to be geometric.
  2. Find Common Ratio: Find the common ratio in the geometric sequence. Two consecutive terms are 66 and 3636. 366=6\frac{36}{6} = 6 Common Ratio: 66
  3. Calculate Missing Number: We multiply each term by the common ratio to get the next term. \newlineSequence: 66, 3636, 216216, _____, 7,7767,776 \newlineCommon Ratio: 66 \newlineFind the missing number in the sequence. \newlineThe number before the missing term is 216216. \newline216×6=1,296216 \times 6 = 1,296 \newlineMissing Number: 1,2961,296
  4. Verify Sequence: Verify the sequence with the missing number filled in. \newlineSequence: 6,36,216,1,296,7,7766, 36, 216, 1,296, 7,776\newlineCheck if 1,2961,296 multiplied by the common ratio 66 gives the next term 7,7767,776. \newline1,296×6=7,7761,296 \times 6 = 7,776\newlineThe sequence is correct.

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