Question

SOLVE : 2-3 + 4-5 + 6-7....................+40 ?

Answer 1

-41 (if we are to find ?)
+21 (if we are to find the sum of the sequence as written)
-20 (as above with the pattern is continued to the last term)

Explanation:

Here we have a somewhat ambigious question.

Either we are to simply find a value for "?"

Or if we are to find the sum of the sequence.
Here, to follow the pattern of the first three pairs you would expect the last pair to be 40-41. However, question tells us that the last term of the sum is 40.

I will answer all of these possibilities in turn.

A. Find ?

This is the most simple case.
Since we have a sequence of consecutive natural numbers with alternating sign the last term will be `-41`

B. Find the sum of the sequence as written:

`2-3 + 4-5 + 6-7 + ......... +40`

Here we have pairs of numbers of the form:

`(2i - (2i+1))` for `i = 1 to n`

Since the last term is 40 the last pair must be `38-39`

Which implies `n=38/2 = 19`

Since each pair sums to `-1`

Sum `= 19xx(-1) +40 = -19+40 = +21`

C. Find the sum of the sequence if pattern is maintained.

Here the last pair would be `40-41` (See A above)

Hence: `n=40/2 = 20`

Sum `= 20xx(-1) = -20`