Question
Download Solution PDFLet a, b, c be in AP and k ≠ 0 be a real number. Which of the following are correct?
1. ka, kb, kc are in AP
2. k - a, k - b, k - c are in AP
3. \(\frac{a}{k},\frac{b}{k},\frac{c}{k}\) are in AP
Select the correct answer using the code given below:Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
1. If a, b and c are in A.P
- Then ka, kb, kc are in AP
- eg. 2, 4, 6 are in A.P then (2 × 2, 4 × 2, 6 × 2) = (4, 8, 12) are also in A.P
2. If a, b and c are in A.P
- Then k - a, k - b, k - c are in AP
- eg. 2, 4, 6 are in A.P then (8 - 2, 8 - 4, 8 - 6) = (6, 4, 2) are also in A.P
3. If a, b and c are in A.P
- Then \(\frac{a}{k},\frac{b}{k},\frac{c}{k}\) are in AP
- eg. 2, 4, 6 are in A.P then (2/2, 4/2, 6/2) = (1, 2, 3) are also in A.P
- Hence, All the options are correct.
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