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Three number are in A.P, such that their...

Three number are in A.P, such that their sum is 18 and sum of there square is 158. The greatest among them is

A

10

B

11

C

12

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let the number be a-d,a,a+d. Then,
`3a=18rArra=6`
`(a-d)^(2)+a^(2)+(a+d)^(2)=158`
`rArr" "3a^(2)+2d^(2)=158`
`rArr" "108+2d^(2)=158rArr2d^(2)=50rArrd=pm5`
Hence, the numbers are : 1,6,11. So, the greatest number is 11.
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
  1. Three number are in A.P, such that their sum is 18 and sum of there sq...

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  2. Let H(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n), then the sum to n terms...

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  3. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

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  4. If A(1),A(2) are between two numbers, then (A(1)+A(2))/(H(1)+H(2)) is ...

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  5. If the (m+1)t h ,(n+1)t h ,a n d(r+1)t h terms of an A.P., are in G.P....

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  6. Given that n arithmetic means are inserted between two sets of numbers...

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  7. If a,b, and c are in G.P then a+b,2b and b+ c are in

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  8. If in a progression a1, a2, a3, e t cdot,(ar-a(r+1)) bears a constant...

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  9. If in an AP, t1 = log10 a, t(n+1) = log10 b and t(2n+1) = log10 c then...

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  10. Find the sum of the series: 1^2-2^2+3^2-4^2+.....-2008^2+2009^2.

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  11. If 4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)," where "a,b,c are non-zero nu...

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  12. If Sn denotes the sum of n terms of an A.P. whose common difference is...

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  13. The sides of a right angled triangle are in A.P., then they are in the...

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  14. Find the sum of all the 11 terms of an AP whose middle most term is 30...

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  15. The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...

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  16. If three numbers are in G.P., then the numbers obtained by adding the ...

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  17. If p ,q ,r are in A.P., show that the pth, qth and rth terms of any G....

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  18. Let a,b,c be three positive prime number. The progrrssion in which sqr...

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  19. If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a...

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  20. If three numbers are in H.P., then the numbers obtained by subtracting...

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  21. The first three of four given numbers are in G.P. and their last three...

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