Question

Arithmetic progression find the sum of 10+20+30+40..............200

Answer 1

therefore sum of 10+20+30+40..............200 is 2100.

Answer 2

Answer:

The sum of 10+20+30+40..............200 is 2100.

Step-by-step explanation:

The given AP

10+20+30+40..............200

Here, first term is 10 and common difference is 10.

The nth term of an AP is

$a_n=a+(n-1)d$

$200=10+(n-1)(10)$

$200-10=(n-1)(10)$

$190=(n-1)(10)$

$19=(n-1)$

$19+1=n$

$n=20$

Number of terms is 20.

The sum of n terms of an AP.

$S_n=\frac{n}{2}[2a+(n-1)d]$

$S_{20}=\frac{20}{2}[2(10)+(20-1)(10)]$

$S_{20}=10\times [20+190]$

$S_{20}=10\times 210$

$S_{20}=2100$

Therefore the sum of 10+20+30+40..............200 is 2100.