Need help with this series sum problem.

[nbtaher]

What is the sum of following series if, the number of terms is 192.
4 + (-8) + 9 + (-10) + 11 + (-12) + ..... = ?

I can see that it is neither an arithmetic nor a geometric sequence.
Starting from n=2, taking every other n makes a sequence.
Starting at n=3, taking every other n after that also makes a sequence.
But I still can't figure out how to get to the solution. The sum is supposed to be -99.

 

[Deleted member 4993]

What is the sum of following series if, the number of terms is 192.
4 + (-8) + 9 + (-10) + 11 + (-12) + ..... = ?

I can see that it is neither an arithmetic nor a geometric sequence.
Starting from n=2, taking every other n makes a sequence.
Starting at n=3, taking every other n after that also makes a sequence.
But I still can't figure out how to get to the solution. The sum is supposed to be -99.

Note [(-8) + (9)] + [(-10) +11] + ... = 1 +1 .....

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[JeffM]

You are very close.

4 - 8 + 9 - 10 + 11 - 12 … = 4 - 8 + (9 + 11 + …) - (10 + 12 + ) = -4 + plus an arithmetic series in m minus an arithmetic series in n is one way to go.

Alternatively and even more simply, 4 - 8 + 9 - 10 + 11 - 12 = 4 - 8 + (9 - 10) + (11 - 12) + …

Tricky third alternative

- 4 + (-8 + 9) + (- 10 + 11) + … what?

 

[Dr.Peterson]

What is the sum of following series if, the number of terms is 192.
4 + (-8) + 9 + (-10) + 11 + (-12) + ..... = ?

I can see that it is neither an arithmetic nor a geometric sequence.
Starting from n=2, taking every other n makes a sequence.
Starting at n=3, taking every other n after that also makes a sequence.
But I still can't figure out how to get to the solution. The sum is supposed to be -99.

Do we know for sure what the pattern is? If the first term were 7 instead of 4, we'd have 7, 9, 11, ... and -8, -10, -12, ... which are two arithmetic sequences; but the 4 means all bets are off.

But if we take it as arithmetic after the 4, then pairing terms starting either with (-8+ 9) or (9 + -10) makes a very easy sum.

 

[bigjohn 2]

Let A = sum of the 192 terms.....add 8-4 to both sides to have 190 term = A + 4.....then pairing the rest you have 190/2 terms of (-1)...easy to find A