Correct Answer: – 300

Solution : The given expression alternates between adding and subtracting the numbers 1, 7, 2, 8, 3, 9, 4, 10, and so on.
We can observe that the numbers being added increase by 1 each time, while the numbers being subtracted also increase by 1 each time.
To find the value of the expression to 100 terms, group the terms into pairs.
Each pair consists of a positive number and its negative counterpart.
The sum of each pair is always – 6 because (–7 + 1 = – 6, – 8 + 2 = – 6, – 9 + 3 = – 6, and so on).
Since we have 100 terms in total, we can form 50 pairs.
Each pair sums up to – 6, so the sum of the 100 terms is = 50 pairs × (–6) = –300
$\therefore$ The value of the expression 1 – 7 + 2 – 8 + 3 – 9 + 4 – 10 + ... to 100 terms is – 300.
Hence, the correct answer is – 300.