Final answer:
After calculating the sum for each expression, they are arranged in increasing order: Expression D with value 1, Expression C with value 15, Expression B with value 24, and Expression A with value 46.
Step-by-step explanation:
Arranging the Summation Expressions
To arrange the summation expressions in increasing order of their values, we must first calculate the sum of each expression, which involves basic arithmetic and knowledge of summation properties.
Expression D, sumᵢ=1¹ (i²), simplifies to just 1² = 1, since there is only one term when i=1.
Expression C, sumᵢ=1² (5i), simplifies to 5×1 + 5×2 = 5 + 10 = 15.
Expression B, sumᵢ=1³ (4i), simplifies to 4×1 + 4×2 + 4×3 = 4 + 8 + 12 = 24.
Expression A, sumᵢ=1⁴ (5i - 1), simplifies to (5×1 - 1) + (5×2 - 1) + (5×3 - 1) + (5×4 - 1) = 4 + 9 + 14 + 19 = 46.
Now, we can arrange the sums in increasing order: D, C, B, A.
The correct order is 1, 15, 24, 46 for expressions D, C, B, and A respectively.