Question

If ∑ (3 + )
7
=4 = 74, find the value of k.

Answer 1

To find the value of k in the given expression, we substitute the given values and solve for k. The value of k is 129.5.

Step-by-step explanation:

To find the value of k in the given mathematical expression ∑ (3 + )/7, where ranges from 4 to 7 and the sum equals 74, we need to substitute the given values into the expression and solve for k.

1. When = 4, the expression becomes (3(4) + )/7 = (12 + )/7.
2. Similarly, when = 5, the expression becomes (3(5) + )/7 = (15 + )/7.
3. When = 6, the expression becomes (3(6) + )/7 = (18 + )/7.
4. Finally, when = 7, the expression becomes (3(7) + )/7 = (21 + )/7.

Since the sum of these four expressions is equal to 74, we can now set up the equation:

(12 + )/7 + (15 + )/7 + (18 + )/7 + (21 + )/7 = 74

Simplifying the equation, we can collect the terms and solve for k:

12 + 15 + 18 + 21 + 4 = 74 * 7

66 + 4 = 74 * 7

4 = 74 * 7 - 66

4 = 518

= 518/4

= 129.5

Therefore, the value of k in the given expression is 129.5.

Learn more about Solving an algebraic expression