Question

There are n arithmetic means between 3 and 54, find n

Answer 1

Answer:

n=16

Step-by-step explanation:

Let the 1st term=a and common difference=d  

there are n arirthmatic mean  

so total number of terms= (n+2)  

so the last term  

=a+(n+2-1)d =a+(n+1) d=54  

4th arithmatic mean=5 th term  

=a+(5-1)d  

=a+4d  

=3+4d  

and (n-2) th arithmatic mean=(n-2+1) =(n-1) th term  

=a+(n-1-1)d = a + (n-2)d =a + (n+1)d -3d =54-3d  

now  

[(3+4d)/(54-3d)] =  

1/3  

after solving  

we will get  

15d=45  

d=3  

now put the value of a and d in the equation  

a+(n+1) d=54  

or, 3+(n+1)3=54  

or,(n+1)3=51  

or,(n+1)=17  

or,n=16  

Answer 2

Answer:

Step-by-step explanation: