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Find the sum of the first 5 terms of the series 1, 4, 9, 16, ...
Find the sum of the first 5 terms of the series 1, 4, 9, 16, ...
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Practice Questions
1 question
Q1
Find the sum of the first 5 terms of the series 1, 4, 9, 16, ...
30
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33
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The series is the sum of squares: 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 1 + 4 + 9 + 16 + 25 = 55.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the sum of the first 5 terms of the series 1, 4, 9, 16, ...
Solution:
The series is the sum of squares: 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 1 + 4 + 9 + 16 + 25 = 55.
Steps: 5
Show Steps
Step 1: Identify the series. The series is 1, 4, 9, 16, ...
Step 2: Recognize that these numbers are the squares of the first 5 natural numbers: 1^2, 2^2, 3^2, 4^2, 5^2.
Step 3: Write down the squares: 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25.
Step 4: Add these squares together: 1 + 4 + 9 + 16 + 25.
Step 5: Calculate the sum: 1 + 4 = 5, then 5 + 9 = 14, then 14 + 16 = 30, and finally 30 + 25 = 55.
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