Question

Evaluate

Answer 1

Answer:

$S_{21}=8.4$

Step-by-step explanation:

Sum Of Arithmetic Sequences

Given a sequence

$a_1, a_1+r, a_1+2r, ...., a_1+(n-1)r$

The  sum of all terms is

$\displaystyle S_n=n\frac{a_1+a_n}{2}$

$a_n=a_1+(n-1)r$

If we know $a_n, a_1, r$

we can compute n as

$\displaystyle n=\frac{a_n-a_1}{r}+1$

The given sequence is

$0.30+0.31+0.32+...+0.50$

The common difference is

$r=0.31-0.30=0.01$

$a_1=0.30, a_n=0.50$

We compute n

$\displaystyle n=\frac{0.50-0.30}{0.01}+1$

n=21

So the given sum is

$\displaystyle S_{21}=21\frac{0.30+0.50}{2}$

$S_{21}=21(0.40)$

$S_{21}=8.4$