Question

Find the sum of the summation of 3 i minus 15, from i equals 2 to 7.

Answer 1

The summation symbol means we use the variable i in the equation from the given range. In this case, we are given with the equation 3 i - 15 and i ranges from 2 to 7. The summation using simply the calculator is equal to -9. The answer to this problem is -9.

Answer 2

Answer:

$\sum _{i=2}^73i-15=-9$

Step-by-step explanation:

Given : $\sum _{i=2}^73i-15$

We have to evaluate the given summation.

Consider $\sum _{i=2}^73i-15$

using, we have,

$\sum _{k=m}^n\:=\:\sum _{k=1}^n\:-\:\sum _{k=1}^{m-1}$

$=\sum _{i=1}^73i-15-\sum _{i=1}^13i-15$      ..............(1)

Consider, $\sum _{i=1}^73i-15$

Apply sum rule,

$\quad \sum a_n+b_n=\sum a_n+\sum b_n$ , we have,

$=\sum _{i=1}^73i-\sum _{i=1}^715$

Now, first consider, $\sum _{i=1}^73i$

Apply constant multiplication rule,$\quad \sum c\cdot a_n=c\cdot \sum a_n$ we have,

$=3\cdot \sum \:_{i=1}^7i$

$=3\cdot \:28\\\\=84$

Also, $\sum _{i=1}^715=105$

Thus, $\sum _{i=1}^73i-15=84-105=-21$

Similarly, $\sum _{i=1}^13i-15=-12$

Substitute in (1) , we have,

Thus, $\sum _{i=2}^73i-15=-21-(-12)=-21+12=-9$

Thus, $\sum _{i=2}^73i-15=-9$