Questions
The three numbers a, b, c between 2 and 18 are such that their sum is 25; the numbers 2, a, b are consecutive terms of an A.P. and the numbers b, c, 18 are consecutive terms of a G.P. The three numbers are
detailed solution
Correct option is C
we have a+b+c=25 (1)∵2,a,b are in A.P., ∴ 2a=2+b (2)∵b,c18 are in G.P., ∴ c2=18b (3)From Eq. (1) and (2), 3b+2c=48; or 3b=48−2c∴ From Eq. (3), c2=6(48−2c)=288−12cor c2+12c−288=0or c2+24c−12c−288=0 (∵a=b+12)or 18b=−72∴b=−4,From Eq. (1), a=−4+12=8 Hence, the four numbers are 8, –4, 2 and 8.Similar Questions
If and 1 are in A.P, then x is equal to
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