Find the sum of the summation of 3 i plus2, from i equals 5 to 13.

Solution:

We have to find the sum of the summation of 3 i plus2, from i equals 5 to 13.

So, \(\sum_{i=5}^{13}(3i+2)\)

= \([(3(5)+2)+(3(6)+2)+(3(7)+2)+(3(8)+2)+(3(9)+2)+(3(10)+2)+(3(11)+2)+(3(12)+2)+(3(13)+2)]\)

= \([(15+2)+(18+2)+(21+2)+(24+2)+(27+2)+(30+2)+(33+2)+(36+2)+(39+2)]\)

= \([17+20+23+26+29+32+35+38+41]\)

= 261

Therefore, the sum of the summation is 261.

Find the sum of the summation of 3 i plus2, from i equals 5 to 13.

Summary:

The sum of the summation of 3 i plus2, from i equals 5 to 13 is 261.