# Is this correct? Arithmetic sum and sequence sum_(n=51)^100 7n

## ${\sum}_{n = 51}^{100} 7 n$ ${S}_{n} = \frac{50}{2} \left(357 + 700\right) = = 26 , 425$ a_100=7(51)+7(100−51)=700

Apr 19, 2018

See below.

#### Explanation:

You need the sum from $n = 51$ so:

${\sum}_{n = 1}^{100} 7 n - {\sum}_{n = 1}^{50} 7 n$

$7 \cdot \left({\sum}_{n = 1}^{100} n - {\sum}_{n = 1}^{50} n\right)$

$7 \cdot \left(\frac{100}{2} \left(2 + 99\right) - \frac{50}{2} \left(2 + 49\right)\right)$

$7 \cdot \left(5050 - 1275\right)$

$7 \cdot \left(3775\right) = 26425$

${n}_{100}$

First term is 7 and common difference is 7:

$n t h$ term

$a + \left(n - 1\right) d$

${n}_{100} = 7 + \left(99\right) \cdot 7 = 700$

So you are correct, or we are both wrong.