Class 10

Math

All topics

Arithmetic Progressions

In a zoo, there are $210$ visitors on first day, $250$ visitors on second day and $290$ visitors on third day, and so on in an arithmetic sequence. What is the total number of visitors on $15_{th}$ day?

- $7,960$
- $7,250$
- $7,660$
- $7,350$

$a=210,d=40$

First find the common difference:

$a_{n}=a_{1}+(n−1)d$

$a_{15}=210+(15−1)40$

$=210+14×40$

$a_{15}=770$

We know that, $S_{n}=2n $ [First term $+$ Last term]

$=215 [210+770]$

$=7.5[980]$

$S_{15}=7,350$

So, the total number of visitors on $15_{th}$ day is $7,350$.