A.P

Algebra Level pending

The sum of three positive numbers in an arithmetic progression is 27, and the sum of their squares is 293. Let λ , μ , ξ \lambda, \mu, \xi denotes these three numbers in that order. Submit your answer as λ 2 ξ + 2 μ \lambda^2 - \xi + 2 \mu .


The answer is 20.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Syed Baqir
Aug 27, 2015

a + a-d + a+d = 27 => 3a = 27 => a=27/3 = 9

and (9-d)^2 + 81 + (9+d)^2 = 293 => d = +- 5

Hence , 9 - 5 = 4 ,

Similarly, Second term = 9 and third = a + d = 9 + 5 = 14

Hence: (\lambda )^{ 2 }-(\xi )+2 \mu = (4)^2 - 14 + 2 (9) = 20

It is already given in the question that their sum is 27. Why bother working out the values?

Pi Han Goh - 5 years, 9 months ago

Log in to reply

The main emphasis was the first three terms , I will edit my question, thanks

Syed Baqir - 5 years, 9 months ago

Could the answer be both 20 and 210? It did not say anything about whether d = 5 or -5.

Saya Suka - 4 years, 7 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...