Arithmetic means are inserted between 1 and 50 so that the sum of the resulting arithmetic progression is 561.
(a) How many arithmetic means were inserted?
(b) What is the common difference of the resulting arithmetic progression?

Question

Arithmetic means are inserted between 1 and 50 so that the sum of the resulting arithmetic progression is 561.
(a) How many arithmetic means were inserted?
(b) What is the common difference of the resulting arithmetic progression?

anonymous · Answer

here clearly the first term is 1 and the last term is 50
thes sum of AP whose first and last term is given= (n/2)*(first term +last term)

anonymous · Answer

hence the number of term=2*561/(1+50) =2*561/51=2*11=22
50=1+(11-1)*d
d is the common difference

anonymous · Answer

Isn't it 50=1+(22-1)d?

anonymous · Answer

THANKYOOOU. :)

jack1 · Answer

wait... was the answer as @puuhreey said:

50=1+(22-1)d so d = 49/21 = 2.333

or was it as @matricked said and :

50=1+(11-1)*d so d = 49/10 = 4.9 ...?