Evaluate the Summation sum from i=1 to 16 of 3i+2

Problem

(∑_i=1^16)(3*i+2)

Solution

1. Identify the type of sequence being summed. The expression 3*i+2 is linear in terms of i which indicates an arithmetic series.

2. Determine the number of terms n Since the index i goes from 1 to 16 there are n=16 terms.

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

(a_1)=3*(1)+2=5

4. Calculate the last term (a_16) by substituting i=16 into the expression.

(a_16)=3*(16)+2=50

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

(S_16)=(16*(5+50))/2

6. Simplify the expression to find the final sum.

(S_16)=8*(55)=440

Final Answer

(∑_i=1^16)(3*i+2)=440

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