Question

Find the sum of the first 100 terms of the A.P. \[14, 16, 18, \ldots\]

Options

• \[11{,}300\]

• \[10{,}300\]

• \[22{,}600\]

• \[11{,}200\]

Answer 1

Here \[a = 14,\ d = 2,\ n = 100.\] Using \[S_n = \frac{n}{2}[2a + (n-1)d],\] we get \[S_{100} = \frac{100}{2}[2(14) + (100-1) \times 2] = 50[28 + 198] = 50 \times 226 = 11{,}300.\]