Find the indicated partial sum for the given sequence.
-$\mathrm { s } _ { 10 } , - 77 , - 117 , - 157 , - 197 , \ldots$
A) 1030
B) $- 2185$
C) $- 2570$
D) 2185

Question

Quizplus · Accepted Answer

The sequence is an arithmetic sequence with first term $\mathrm{s}_{10} = a = 1030$ and common difference $d = -40$.

Using the formula for the partial sum of an arithmetic sequence, we have:

$$\mathrm{S}_n = \frac{n}{2}(2a + (n-1)d)$$

For this problem, $n=10$, $a=1030$, and $d=-40$. Substituting the values in the formula, we get:

$$\mathrm{S}_{10} = \frac{10}{2}(2\cdot 1030 + (10-1)\cdot (-40)) = -2570$$

Therefore, the best choice is $\boxed{	extbf{(C)}\ -2570}$.

Find the Indicated Partial Sum for the Given Sequence s10,−77,−117,−157,−197,…\mathrm { s } _ { 10 } , - 77 , - 117 , - 157 , - 197 , \ldotss10​,−77,−117,−157,−197,…

Find the Indicated Partial Sum for the Given Sequence $\mathrm { s } _ { 10 } , - 77 , - 117 , - 157 , - 197 , \ldots$