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Question

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


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, yx = 10 − (− 20) = 10 + 20 = 30.

Mathematics
RD Sharma (2020, 2021)
All

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