Question

Find the sum of the summation of 2 i minus 12, from i equals 7 to 16.

22
110
220
440

Answer 1

Answer: Second option is correct.

Explanation:

Since we have given that

`\sum_(7)^(16)(2i-12)\\\\=\sum_(7)^(16)2(i-6)\\\\=2\sum_(7)^(16)(i-6)\\\\=2[(16-6)+(15-6)+(14-6)+(13-6)+(12-6)+(11-6)+(10-6)+(9-6)+(8-6)+(7-6)]\\\\=2[10+9+8+7+6+5+4+3+2+1]\\\\\text{Sum of n natural numbers }\\\\=2((10* (10+1))/(2))\\\\\=(n(n+1))/(2)\\\\=2* (10* 11)/(2)\\\\=10* 11\\\\=110`

Hence, the value of summation is 110.

Therefore, Second option is correct.

Answer 2

Sum: S
S=[2(7)-12]+[2(8)-12]+[2(9)-12]+[2(10)-12]+[2(11)-12]+[2(12)-12]+[2(13)-12]+[2(14)-12]+[2(15)-12]+[2(16)-12]

S=2(7+8+9+10+11+12+13+14+15+16)-10(12)
S=2(115)-120
S=230-120
S=110

Answer: Second option 110