Question

use the formula for finding the sum 1 + 2 + 3 + … + n to discover a formula for finding the sum 10 + 20 + 30 + … + 10n. the formula for the sum 10 + 20 + 30 + … + 10n is s = (simplify your answer. use whole numbers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the known sum formula

The sum of the first $n$ positive integers is given by:
$$1+2+3+\dots+n = \frac{n(n+1)}{2}$$

Step2: Factor out the common term

Factor 10 from the sum $10+20+30+\dots+10n$:
$$10+20+30+\dots+10n = 10(1+2+3+\dots+n)$$

Step3: Substitute the known formula

Replace $1+2+3+\dots+n$ with $\frac{n(n+1)}{2}$:
$$10+20+30+\dots+10n = 10 \times \frac{n(n+1)}{2}$$

Step4: Simplify the expression

Calculate $10 \times \frac{1}{2} = 5$:
$$10+20+30+\dots+10n = 5n(n+1)$$

Answer:

$5n(n+1)$