calculator\nwhat is $sum_{n=1}^{11} (98 - 2n)$ equal to?\nenter your answer in the box.
calculator\nwhat is $sum_{n=1}^{11} (98 - 2n)$ equal to?\nenter your answer in the box.
Answer
Answer:
968
Explanation:
Step1: Identify the sum formula
The given expression is a sum of an arithmetic progression. $$ \sum_{n=1}^{11} (98 - 2n) $$
Step2: Calculate the first term
Substitute $n=1$ into the expression to find the first term $a_1$. $$ a_1 = 98 - 2(1) = 98 - 2 = 96 $$
Step3: Calculate the last term
Substitute $n=11$ into the expression to find the last term $a_{11}$. $$ a_{11} = 98 - 2(11) = 98 - 22 = 76 $$
Step4: Determine the number of terms
The number of terms is given by the upper limit of the summation, which is $N=11$.
Step5: Apply the sum formula
The sum of an arithmetic progression is given by $S_N = \frac{N}{2}(a_1 + a_N)$. $$ S_{11} = \frac{11}{2}(96 + 76) $$
Step6: Calculate the sum
Perform the addition and multiplication. $$ S_{11} = \frac{11}{2}(172) = 11 \times 86 = 946 $$