Answer:
n = -15
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