Question

5+(-41)+9+(-39)+13+(-37)+17+....+(-5)+81+(-3)
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Answer 1

Answer:

the given series is 5+ (-41) + 9 + (-39) + 13 + (-37) + 17+ .....

it consists of two ap's

S1 = 5 + 9 + 13+....+77+81, where a=5, d=4

S2=−41−39−37−...(−3), where a=−41 and d=2

for S1,81=5+(n−1)×4⇒n−1=764,hence n=20

S20=202×[5+81]=10×86=860for S2,−3=−41+(n−1)×2⇒n−1=382,

hence

n=20

S20=202×[−41−3]=−10×44=−440Total sum=S1+S2=860−440=420Answer=420