Question

(Incomplete sol.)

Between two no. whose sum is 2 1/6 an even number of arithmetic means is inserted; the sum of these means exceeds their numbers by 1. How many means are there?
@nitz

Answer 1

suppose two numbers are a and b
a+b=6

Answer 2

it is 2+1/6

Answer 3

13/2

Answer 4

suppose n means are inserted.
and average of all arithmatic means will be same as of whole seriese irrespective of number of a.m.
so,average =(a+b)/2=3

Answer 5

ya 13/2

Answer 6

s0rry a+b=13/2
and average is 13/4

Answer 7

"average of all arithmatic means will be same as of whole seriese " , how?

Answer 8

is it like , in an AP of x,y,z
y=(x+z)/2

Answer 9

??

Answer 10

wait...i am myself confused

Answer 11

ok lets try another method

let n be the total number of terms in the series and hence n-2 is the no. of means
sum of means=n/2(a+1)-(a+1)
number of means=n-2

Answer 12

right till here?

Answer 13

sum of means , how it came?

Answer 14

from statement.....read again

Answer 15

no i am confused.

Answer 16

write that in fractions

Answer 17

what in fractions?

Answer 18

nothing

Answer 19

(a+1)-(a+1) how it came.

Answer 20

it should be a+1+b-1

Answer 21

so the sum \[\frac{n(a+b)}{2}\]