5+(−41)+9+(−39)+13+(−37)+17+....+(−5)+81+(−3)
The given series is combination of two AP’s.
Let A1​=5+9+13+.....+77+81
and A2​=−41−39−37−......(−3)

For A1​:
First term =a=5
Common difference=d=2
Last term =l=81
Now, using formula:
81=5+(n−1)4
n=20
Thus, there are 20 terms in AP.
Now,
Find the sum of these 76 terms:
S20​=n/2[a+l]
=20/2(5+81)
=860
Sum of 20 terms of this AP is 860.

For A2​:
First term =a=−41
Common difference =d=2
Last term=l=3
Now, using formula:
−3=−41+(n−1)2
n=20
Thus, there are 20 terms in AP.
Now,
Find Sum of these 76 terms:
S20​=n/2[a+l]
=20/2(−41−3)
=−440
Sum of 20 terms of this AP is −440.

Therefore, Sum of total terms: 860−440=420.