Answer:
13
Step-by-step explanation:
Its calculate the common difference first.
(95-11)/(n-1).
We also have the sum of these n terms is 689.
So we have the following:
11
+(11+(95-11)/(n-1))
+(11+2(95-11)/(n-1))
+...
+(11+(n-1)(95-11)/(n-1))
This can be re-expressed alittle:
There are (n) amount of 11's in the addition... also 1+2+3+...+(n-1)=(n-1)(n)/2.
So we have the sum is
11(n)+n(n-1)/2×(95-11)/(n-1)
But this equal to 689.
We need to solve the following equation:
11(n)+n(n-1)/2×(95-11)/(n-1)=689
The (n-1)'s in second term can cancel.
11(n)+n/2×84=689
11n+42n=689
53n=689
53n=689
n=689/53
n=13
