Question 1158007

Hi

The sum of 3 terms of an arithmetic progression is 42 and the product of the 
First and third term is 52.

Find the 3 terms.

Thanks 
<pre>I totally agree with TUTOR @IKLEYN!

Middle term of this 3-term A.P., or MEAN = {{{matrix(1,3, 42/3, "=", 14)}}}
Therefore, 1st term = 14 - d, and 3rd term = 14 + d

As the PRODUCT of the 1st and 3rd terms = 52, we get: (14 - d)(14 + d) = 52
                                                      {{{matrix(3,3, 196 - d^2, "=", 52, 
196  -  52, "=", d^2,
144, "=", d^2)}}}
                                                      Common difference, or {{{matrix(1,3, d, "=", ""+- 12)}}}
d = 12
1<sup>st</sup> term: 14 - 12 = 2
2<sup>nd</sup> term: 14 (predetermined)
3<sup>rd</sup> term: 14 + 12 = 26
So, when {{{highlight_green(system(matrix(1,6, d, or, common, difference, "=", 12), matrix(1,6, a[1], or, 1^(st), term, "=", 2)))}}}, and the 3 terms are: {{{highlight_green(matrix(1,4, "2,", "14,", and, 26))}}}

d = - 12
1<sup>st</sup> term: 14 - - 12 = 26
2<sup>nd</sup> term: 14 (predetermined)
3<sup>rd</sup> term: 14 + - 12 = 2
So, when {{{highlight_green(system(matrix(1,6, d, or, common, difference, "=", - 12), matrix(1,6, a[1], or, 1^(st), term, "=", 26)))}}}, and the 3 terms are: {{{highlight_green(matrix(1,4, "26,", "14,", and, 2))}}}</pre>