Question

Find the value of y if the arithmetic mean of 3 and 3y + 5 is 8. Determine the arithmetics sequence and the common difference.​

Answer 1

Answer:

Find the value of y if the arithmetic mean of 3 and 3y + 5 is 8. Determine the arithmetics sequence and the common difference.

Step-by-step explanation:

anwer please

Answer 2

Given: arithmetic mean of 3 and 3y + 5 is 8

To Find: Value of y and determination of arithmetics sequence and the common difference.​

Solution:

Consider a=3 & c= 3y+5

Let a,b & c be in arithmetic progression where b is the arthimatic mean of a & c.

Clearly,b=(a+c)/2 = (3+3y+5)/2

                             =3+3y+5=16

                              3y=8

                               y=8/3

Check:

LHS=arthimatic mean of 3={ 3+ 3(8/3)+5}/2 = (3+13)/2=16=8=RHS

           Hence, y=8/3

1st term =3   2nd term=13

common difference=10

an  =a+(n-1)d

a1   =3+0=3

a2   =3+(2-1)x10=3+10=13      

a3    =3+(3-1)10=3+20=23  

with sequence -->3,13,23,...

Arthimatic sequence=10