Question

Find the sum of the first 28 terms of the following sequence:

-7, -4, -1 . . .
938 1876
134 588

Answer 1

134

Answer 2

This problem is "sequence of numbers with common difference".
Suppose that d is common difference, n is a number of term.
\[a_{1} = -7 = -7 +3(n-1)\]
d = 3. Because the sequence increase by 3.

So when n=28,
\[a_{28} = -7 + 3\times (28 - 1) = -7 + 3 * 27 = 74\]

Therefore, the sum of the first 28 terms is
\[S_{28} = a_{1} + a_{2} +.... + a_{28} = \frac{ n (a_{1} + a_{28}) }{ 2 }\]
\[=\frac{ 28 \times (-7 + 74) }{ 2 } = 14 \times 67 = 938\]

The answer is "938".