If the sum of the integers from 15 to 50, inclusive, is equal to the sum of the integers
from n to 50, inclusive, and n<15, then n=

A)-49
B)-35
C)-15
D-14

n = -15

Step-by-step explanation:

Given

Sum of Integers from 15 to 50 (inclusive) = Sum of integers from n to 50 (inclusive)

n < 15

Required

Find n

We can split the given parameters to 2

i. Sum of Integers from 15 to 50 (inclusive)

ii. Sum of integers from n to 50 (inclusive)

Solving for (i): Sum of Integers from 15 to 50 (inclusive)

We'll make use of sum of n terms of an arithmetic;

This is given as follows

Where n is the number of terms from 15 to 50

T1 is the first term; T1 = 15

Tn is the last term; Tn = 50

n is calculated using

The formula becomes

Solving for (ii): Sum of integers from n to 50 (inclusive)

We'll also make use of the same formula used above

Where n is the number of terms from n to 50

T1 is the first term; T1 = n

Tn is the last term; Tn = 50

n is calculated using

The formula becomes

Recall that the Sum of Integers from 15 to 50 (inclusive) = Sum of integers from n to 50 (inclusive);

This implies that

Sn (i) = Sn (ii)

As such; we have

Multiply both sides by 2

Open Brackets

Reorder

Subtract 2340 from both sides

Multiply both sides by -1

At this point, we have a quadratic equation; as such, it'd be solved as follows:

Expand

Factorize

Split the above expression

The question states that n < 15;

This means that we'll discard the value of n = 14

Hence, n = -15

-8

step-by-step explanation:

your answer is 228

step-by-step explanation:

add the top and bottom bases together, then divide them by 2, then multiply by the height.