Question

What is the median value of the set R, if for every term in the set,
`R_n = R_(n-1) + 3`? (1) The first term of set R is 15. (2) The mean of set R is 36.

Answer 1

36

Explanation:

Given that

`R_n = R_(n+1) +3` is given

First term is 15

This is an arithmetic series with a =15 and d =3

If n is the number of terms, then we have

Sum of n terms = 36 xn = 36n

But as per arithmetic progression rule

`S_n = (n)/(2) [2a+(n-1)d]\\= (n)/(2) [30+(n-1)3]=36n`

`72 = 30+3n-3\\n-=15`

When there are n terms we have middle term is the 8th term

Hence median is 8th term

=
`a_8 = 15+7(3) \\=36`