Evaluate: sum_(n=2)^(4)(3x+3n) Answer:

Given Summation Expression: We are given the summation expression sum_(n=2)^(4)(3x+3n). To evaluate this, we will substitute the values of n starting from 2 and ending at 4 into the expression (3x+3n) and then sum the results.Substitute n = 2: First, let's substitute n = 2 into the expression (3x+3n): 3x + 3(2) = 3x + 6.Substitute n = 3: Next, substitute n = 3 into the expression (3x+3n): 3x + 3(3) = 3x + 9.Substitute n = 4: Finally, substitute n = 4 into the expression (3x+3n): 3x + 3(4) = 3x + 12.Sum Substitutions: Now, we sum the results of the substitutions: (3x + 6) + (3x + 9) + (3x + 12).Combine Like Terms: Combine like terms: 3x + 3x + 3x + 6 + 9 + 12.Simplify Expression: Simplify the expression: 9x + (6 + 9 + 12).Add Constant Terms: Add the constant terms: 9x + 27.

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Algebra 2

Simplify variable expressions using properties

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Q. Evaluate:

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\sum_{n=2}^{4}(3 x+3 n)

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Answer:

Given Summation Expression: We are given the summation expression $\sum_{n=2}^{4}(3x+3n)$ . To evaluate this, we will substitute the values of $n$ starting from $2$ and ending at $4$ into the expression $(3x+3n)$ and then sum the results.
Substitute $n = 2$ : First, let's substitute $n = 2$ into the expression $(3x+3n)$ : $3x + 3(2) = 3x + 6$ .
Substitute $n = 3$ : Next, substitute $n = 3$ into the expression $(3x+3n)$ : $3x + 3(3) = 3x + 9$ .
Substitute $n = 4$ : Finally, substitute $n = 4$ into the expression $(3x+3n)$ : $3x + 3(4) = 3x + 12$ .
Sum Substitutions: Now, we sum the results of the substitutions: $(3x + 6) + (3x + 9) + (3x + 12)$ .
Combine Like Terms: Combine like terms: $3x + 3x + 3x + 6 + 9 + 12$ .
Simplify Expression: Simplify the expression: $9x + (6 + 9 + 12)$ .
Add Constant Terms: Add the constant terms: $9x + 27$ .