Let A_1, A_2, , A_39 be 39 arithmetic means between the numbers 59 and 159.

Question

Let $A_1, A_2, \ldots, A_{39}$ be 39 arithmetic means between the numbers $59$ and $159$. Then the mean of $A_{25}, A_{28}, A_{31}$ and $A_{36}$ is equal to:

Accepted Answer

The full A.P. is $59, A_1,\ldots,A_{39}, 159$ --- a total of $41$ terms, so $40$ common-difference gaps:
$$d = \frac{159-59}{40} = 2.5, \qquad A_n = 59+2.5n.$$

$$A_{25}=121.5,\quad A_{28}=129,\quad A_{31}=136.5,\quad A_{36}=149.$$

$$\text{Mean} = \frac{121.5+129+136.5+149}{4} = \frac{536}{4} = 134.$$

Solutions · 1