If A = 1 - 10 + 3 - 12 + 5 - 14 + 7 + … up to 60 terms, then what is the value of A?
-270
Step 1 — Pair the terms: Group consecutive terms as \((1-10),(3-12),(5-14),\dots\). Each pair has the form \((2k-1)-(2k+8)\).
Step 2 — Sum of each pair:
\[(2k-1)-(2k+8)=-9\]
Step 3 — Number of pairs: 60 terms give \(60/2=30\) pairs.
Therefore \(A=30\times(-9)=\mathbf{-270}\).
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