To find the fifth term in the series 49, 56, 63, …, we can use the pattern that the series follows. In this case, the series follows the pattern of adding 7 to the previous term to get the next term.
We can use this pattern to find the fifth term as follows:
The first term is 49. The second term is 49 + 7 = 56. The third term is 56 + 7 = 63. The fourth term is 63 + 7 = 70.
Therefore, the fifth term in the series is 70.
here are some more examples of finding the nth term in a series using different patterns:
Example 1: Find the 10th term in the series 3, 6, 9, 12, …
Solution: This series follows the pattern of adding 3 to the previous term to get the next term. We can use this pattern to find the 10th term as follows:
The first term is 3. The second term is 3 + 3 = 6. The third term is 6 + 3 = 9. The fourth term is 9 + 3 = 12. ... The tenth term is 33 + 3 = 36.
Therefore, the 10th term in the series is 36.
Example 2: Find the 8th term in the series 5, 10, 15, 20, …
Solution: This series follows the pattern of adding 5 to the previous term to get the next term. We can use this pattern to find the 8th term as follows:
The first term is 5. The second term is 5 + 5 = 10. The third term is 10 + 5 = 15. The fourth term is 15 + 5 = 20. ... The eighth term is 40 + 5 = 45.
Therefore, the 8th term in the series is 45.
Example 3: Find the 6th term in the series 2, 6, 18, 54, …
Solution: This series follows the pattern of multiplying the previous term by 3 to get the next term. We can use this pattern to find the 6th term as follows:
The first term is 2. The second term is 2 * 3 = 6. The third term is 6 * 3 = 18. The fourth term is 18 * 3 = 54. ... The sixth term is 162 * 3 = 486.
Therefore, the 6th term in the series is 486.