Question

Find the sum of the first 50 terms of the arithmetic sequence: 3, -4, -11, -18, . . .

Answer 1

Do you know the formula for the sums of arithmetic sequences? It's this:
\[S=\frac{ n }{ 2 }(2a+(n-1)d)\]Where 'S' is the sum, 'n' is the number of terms, 'a' is the first term, and 'd' is the common difference.

For the sequence given, the first term is 3, so a = 3. The common difference is simply the value that the sequence goes up by or goes down by. Subtract any two consecutive terms to find the common difference. But remember, when subtracting, subtract the first term from the second term from the two consecutive terms. For example, if a sequence is 2, 4, 6, 8...and I decide to subtract the two consecutive terms 2 and 4, then I do 4 - 2, not 2 - 4. So for us, the common difference is: -4 - 3 = -7, so d = -7. We have been asked to find the sum of the first 50 terms, so n = 50. Now we just plug in n = 50, d = -7, a = 3 in to the formula to find the sum of the first 50 terms.\[S=\frac{ 50 }{ 2 }(2(3)+(50-1)(-7))=25(6+49(-7))=25(6-343)=25(-337)=-8425\]Therefore, the sum of the first 50 terms is -8425.

Answer 2

@clairenjones1

Answer 3

-8425 is getting cut off so you only see -842, but the value really is -8425.