Evaluate the Summation sum from i=1 to 22 of 6i-5

Problem

(∑_i=1^22)(6*i−5)

Solution

1. Identify the type of sequence being summed. The expression 6*i−5 is linear in terms of i which means this is an arithmetic series.

2. Determine the number of terms n The sum goes from i=1 to i=22 so n=22

3. Calculate the first term (a_1) by substituting i=1 into the expression.

(a_1)=6*(1)−5=1

4. Calculate the last term (a_22) by substituting i=22 into the expression.

(a_22)=6*(22)−5=132−5=127

5. Apply the formula for the sum of an arithmetic series, which is (S_n)=(n*((a_1)+(a_n)))/2

(S_22)=(22*(1+127))/2

6. Simplify the expression to find the final value.

(S_22)=11*(128)=1408

Final Answer

(∑_i=1^22)(6*i−5)=1408

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