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The first three terms of a geometric sequence are as follows. 5,10,20 Find the next two terms of this sequence. 5,10,20,◻,◻

The first three terms of a geometric sequence are as follows.\newline5,10,20 5,10,20 \newlineFind the next two terms of this sequence.\newline5,10,20,□,□ 5,10,20, \square, \square

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Q. The first three terms of a geometric sequence are as follows.\newline5,10,20 5,10,20 \newlineFind the next two terms of this sequence.\newline5,10,20,□,□ 5,10,20, \square, \square
  1. Calculate Common Ratio: To find the next terms in a geometric sequence, we need to determine the common ratio rr. The common ratio is the factor by which we multiply each term to get the next term. We can find the common ratio by dividing the second term by the first term.\newlineCalculation: r=105=2r = \frac{10}{5} = 2
  2. Find Fourth Term: Now that we have the common ratio, we can find the fourth term by multiplying the third term by the common ratio.\newlineCalculation: 4th4^{\text{th}} term =20×r=20×2=40= 20 \times r = 20 \times 2 = 40
  3. Find Fifth Term: Similarly, we can find the fifth term by multiplying the fourth term by the common ratio.\newlineCalculation: 5th5^{\text{th}} term = 40×r=40×2=8040 \times r = 40 \times 2 = 80
  4. Final Sequence: We have found the fourth and fifth terms of the sequence.\newlineThe sequence now reads: 5,10,20,40,805, 10, 20, 40, 80

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