If x = (− 23) + 22 + (− 23) + 22 + ... + (40 terms) and y = 11 + (− 10) + 11 + (− 10) + ... + (20 terms), then find y − x.

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Solution

x = (− 23) + 22 + (− 23) + 22 + ... + (40 terms)
= (− 23) + (− 23) + ... + (20 terms) + 22 + 22 + ... + (20 terms)
= 20 $×$ (− 23) + 20 $×$ 22
= 20 $×$ (− 23 + 22)
= 20 $×$ (− 1)
= − 20
Now
y = 11 + (− 10) + 11 + (− 10) + ... + (20 terms)
= 11 + 11 + ... + (10 terms) + (− 10) + (− 10) + ... + (10 terms)
= 11 $×$ 10 + (− 10) $×$ 10
= 110 − 100
= 10
Therefore, y − x = 10 − (− 20) = 10 + 20 = 30.

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