Question

an AP contains 5 terms.sum of three terms in the middle is 24.the product of first and last term is 48 find that AP​

Answer 1

required AP will be : 4,6,8,10,12

In this type of questions the main thing we have to concerned towards is the selection of terms.

✤when there are 3 terms in AP the terms taken should be( a-d, a , a+d)

✤when 4 terms we should take ( a-3d, a-d, a+d , a+3d)

✤when 5 terms ( a-2d, a-d, a, a+d, a+2d)

✤when 6 terms (a-5d, a-3d, a-d, a+d, a+3d, a+5d)

NOW, REFER TO THE ATTACHMENT FOR SOLUTION

Answer 2

≡QUESTION≡

Five positive integer are in A.P the sum of middle 3 term is 24 and product of first and fifth term 48. Find the term of A.P.

                                                     

║⊕ANSWER⊕║

Series be a−2d, a−d, a, a+d, a+2d

The sum of first 3 terms

$a - d+a+a+d=24\\3a=24\\a = 8$

$(a+2d)(a-2d) = 48$

$a^{2} - 4d^{2} = 48$

Substitute a = 8

$64 - 4d^{2} = 48\\d^{2} = 16\\d = 2 \\ d = -2$

∴ The AP is 4,6,8,10,12