UPSEE Solved Model Paper 1

Let the three numbers be 𝑎, 𝑎𝑟, 𝑎𝑟2

a+ar+ar2

3

=

14

2

⇒ a(1+r+r2) = 14 ... (I)
𝐴𝑙𝑠𝑜, 𝑎 + 1, 𝑎𝑟 + 1, 𝑎𝑟2 − 1 𝑎𝑟𝑒 𝑖𝑛 𝐴.𝑃.
⇒ 𝑎 + 1 + 𝑎𝑟2 − 1 = 2(𝑎𝑟 + 1)
⇒ 𝑎 + 𝑎𝑟2 = 2𝑎𝑟 + 2
⇒ 𝑎(𝑟2−2𝑟+1) = 2 … . (𝐼𝐼)
(𝐼) ÷ (𝐼𝐼) ⇒

1+r+r2

r2−2r+1

=

14

2

= 7
⇒ 2𝑟2 − 5𝑟 + 2 = 0 ⇒ 𝑟 = 2 𝑜𝑟 𝑟 =

1

2

⇒ 𝑎 = 2 𝑜𝑟 𝑎 = 8
Hence required nos. are 2,4,8, or 8,4,2
Sum of squares = 4 + 16 + 64 = 84