Question

1. -1 +3-5-7 + 9 - 11 - ...-55 +57 - 59 = ? A) -600 b)-300 B) -180 T) -150​

Answer 1

Ответ:

-150

Объяснение:

Нужно найти последовательность

Answer 2

To find the sum of this alternating series, we can group the terms in pairs:

(-1 + 3) + (-5 - 7) + (9 - 11) + ... + (-55 + 57) + (-59)

Now, calculate each pair:

2 - 12 + (-2) + ... + 2 + (-59)

Notice that the sequence of numbers in between the pairs (-2, -2, ...) is an arithmetic sequence with a common difference of -2. To find the number of terms in this sequence, we need to determine how many pairs we have. The series starts with -1 and ends with -59, and each pair includes two numbers, so there are (59 - (-1) + 1) / 2 = 60 pairs.

Now, we can find the sum of the arithmetic sequence:

Sum = Number of Terms * (First Term + Last Term) / 2 Sum = 60 * (-2 + (-59)) / 2 Sum = 60 * (-61) / 2 Sum = -1830

Now, let's add back the numbers we calculated earlier:

(-1 + 3) + (-5 - 7) + (9 - 11) + ... + (-55 + 57) + (-59) = -1830 + 2 + (-59)

Finally, calculate the sum:

-1830 + 2 + (-59) = -1830 - 57 = -1887

So, the sum of the given series is -1887.

None of the provided answer choices (A, B, T) match the correct answer of -1887.