Question

2
The sum of three terms in an AP i8 24
the product of first and last term 28
then find the three terms​

Answer 1

Given:-

• Sum of three terms in an AP is 24.

• Product of first and last term is 28.

To Find:-

• The three terms

Solution:-

Let the three terms in an A.P is be,

• First term = a
• Second term = a + d
• Third term = a + 2d

According to question,

$\sf :\implies\:a + a + d + a + 2d = 24$

$\sf :\implies\:3a + 3d = 24$

$\sf :\implies\:a + d =\dfrac{24}{3}$

$\sf :\implies\:a + d =8$

$\bf :\implies\:a =8-d$ ____{1}

And,

$\sf :\implies\:a(a+2d) = 28$

$\sf :\implies\:a^2+2ad= 28$

Putting Value of a in it,

$\sf :\implies\:(8-d)^2+2d(8-d)= 28$

$\sf :\implies\:64+d^2-16d+16d-2d^2= 28$

$\sf :\implies\:64-d^2= 28$

$\sf :\implies\:d^2= 64-28$

$\sf :\implies\:d^2= 36$

$\sf :\implies\:d= \sqrt{36}$

$\bf :\implies\:d= 6$

Putting value of d in {1},

$\sf :\implies\:a =8-6$

$\sf :\implies\:a =2$

$\sf First\: term = a = 2$

$\sf Second\: term = a + d = 2 + 6 = 8$

$\sf Third\: term = a+2d = 2 + 2×6 = 14$

Hence, The three terms are 2, 8 and 14.

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