If the first term of a harmonic progression is 4 and the common difference of the corresponding arithmetic progression is 2, what is the second term?
Practice Questions
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Q1
If the first term of a harmonic progression is 4 and the common difference of the corresponding arithmetic progression is 2, what is the second term?
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The first term is 4, and the reciprocal is 1/4. The second term's reciprocal will be 1/4 + 2 = 9/4, so the second term is 4/9.
Questions & Step-by-step Solutions
1 item
Q
Q: If the first term of a harmonic progression is 4 and the common difference of the corresponding arithmetic progression is 2, what is the second term?
Solution: The first term is 4, and the reciprocal is 1/4. The second term's reciprocal will be 1/4 + 2 = 9/4, so the second term is 4/9.
Steps: 7
Step 1: Identify the first term of the harmonic progression, which is given as 4.
Step 2: Find the reciprocal of the first term. The reciprocal of 4 is 1/4.
Step 3: Identify the common difference of the corresponding arithmetic progression, which is given as 2.
Step 4: Add the common difference (2) to the reciprocal of the first term (1/4). This gives us: 1/4 + 2.
Step 5: Convert 2 into a fraction with a denominator of 4. So, 2 = 8/4.
Step 6: Now add the two fractions: 1/4 + 8/4 = 9/4.
Step 7: The second term of the harmonic progression is the reciprocal of 9/4. The reciprocal is 4/9.
