Question

In the sequence, 1, 2, 3, -4 1, 2, 3, -4, …, the numbers 1,

2, 3, -4 repeat indefinitely. What is the sum of the first 150

terms?

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Answer 1

To find the sum of the first 150 terms of the sequence 1, 2, 3, -4, which repeats indefinitely, calculate the number of complete cycles within those terms and multiply by the sum of one cycle, then add the sum of the remaining terms.

The sum of first 150 terms is 77.

Step-by-step explanation:

• The question asks us to find the sum of the first 150 terms of the sequence 1, 2, 3, -4, which repeats indefinitely.
• To solve this, we can first find the sum of one cycle of the sequence, which is the sum of 1 + 2 + 3 + (-4) = 2.
• Since the cycle repeats every 4 terms, we can divide 150 by 4 to determine how many complete cycles there are in 150 terms.
• We have 150 ÷ 4 = 37 complete cycles with a remainder of 2 terms.
• Therefore, the sum of the first 150 terms is (37 cycles * sum per cycle) + (remainder terms), which equals 37 * 2 + 1 + 2 = 74 + 3 = 77.

Answer 2

`S=77`

Step-by-step explanation:

So we have the sequence:

1, 2, 3, -4, 1, 2, 3, -4...

This four-number sequence repeats indefinitely.

And we want to find the sum of the first 150 terms.

Note that 150 is equivalent to 148+2.

148 is the same as 4(37).

In other words, our sum is the (1,2, 3, -4) sequence 37 times and then plus the first two numbers of the sequence (1 and 2).

So, our sum is:

`S=37(1+2+3+(-4))+(1+2)`

Add:

`S=37(2)+(3)`

Multiply:

`S=74+3`

Add:

`S=77`

So, our sum is 77.