Evaluate this is hard

Question

^{∑ on top is 21 on bottom is k=4 next to the sign is 59-7k}

Answer 1

    21

     ∑     59-7k

   k=4

 

That means to find the sum of the series from k=4 to k=21.

 

You can plug in each individual number from 4 to 21 and add them all up but that will take a very long time so instead we will use these two equations:

 

(1)

 

a_n = a₁ (n-1)d

 

a_n = the last value n you want to find in this case 21, a₁ to the first term which if you plug in 4 you get 35,

n = number of terms in this case it is n = 18, d= difference between terms which is -7.

 

(2)

 

S = (n (a₁ + a_n ))/2

 

S = total sum

 

We use equation (1) to find the a₂₁ term.

 

= 35 + (18-1)(-7) = -84

 

Now we use equation (2) to find the sum:

 

S = (18( 35 - 84))/2 = -441