Grade 12Magical Mathematics[Interesting Approach]

please do this problem

BOLLU SRINIVAS

10 Years agoGrade 12

6 Answers

RAKESH CHINDAM

10 Years ago

let A 1 , A 2 , A 3 , A 4 ......A n be n Arithmetic means are instead between 20 and 80.
i.e., 20 , A 1 , A 2 , A 3 , A 4 ......A n 80.
∴ The Arithmetic Progression consist of ' n + 2 'terms.
let 'd' be the common difference.
The first term a = 20
The last term L = 80.
but the last term is T n + 2 = a + (n + 2 − 1)d
= a + (n + 1)d
T n + 2 = 80
a + (n + 1)d = 80
20 + (n + 1)d = 80
(n + 1)d = 60
d=60/n+1
Given that the ratio of the first mean to the last mean is 1:3
i.e.,A1/An=1/3

20 + d/20 + nd=1/3
(A n = T n + 1 = a + nd)
20 +60/n+1/20+n.60/n+1
3(n + 4) = (4n + 1)
3n + 12 = 4n + 1
n = 11.

T.kumar

10 Years ago

hi bollu srinivas.. The Arithmetic Progression consist of ' n + 2 'terms.let 'd' be the common difference.The first term a = 20The last term L = 80.but the last term is T n + 2 = a + (n + 2 − 1)d= a + (n + 1)dT n + 2 = 80a + (n + 1)d = 8020 + (n + 1)d = 80(n + 1)d = 60d=60/n+1

SAI SARDAR

10 Years ago

Srinivas, The solution of above question is 11.It is from you can do the problem by the formula of arithematic mean and take ratio.

Ankit Jaiswal

10 Years ago

hi Srinivas, The solution of above question is 11.It is from you can do the problem by the formula of arithematic mean and take ratio.

manmath

10 Years ago

hii

let A 1 , A 2 , A 3 , A 4 ......A n be n Arithmetic means are instead between 20 and 80. i.e., 20 , A 1 , A 2 , A 3 , A 4 ......A n 80. ∴ The Arithmetic Progression consist of ' n + 2...yes or no