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Standard X
Mathematics
Arithmetic Progression
Determine k s...
Question
Determine k so that k^2 + 4k + 8,2k^2 + 3k + 6,3k^2 + 4k + 4 are three consecutive terms of an A.P.
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Solution
Since, k
2
+ 4k + 8,2k
2
+ 3k + 6 and 3k
2
+ 4k + 4 are consecutive terms of an AP
∴ 2k
2
+ 3k + 6 – (k
2
+ 4k + 8) = 3k
2
+ 4k + 4 – (2k
2
+ 3k + 6) = Common difference
⇒ 2k
2
+ 3k + 6 - k
2
- 4k - 8 = 3k
2
+ 4k + 4 - 2k
2
- 3k - 6
⇒ k
2
- k - 2 = k2 + k - 2
⇒ -k = k ⇒ 2k = 0
⇒ k = 0
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