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
The number of the terms for the arithmetic series is 13.
The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
The formula for calculating the sum of the arithmetic progression.
Sn = ( n / 2 ) [ a₁ + a[tex]_{n}[/tex]]
689 = ( n / 2 ) [ 11 + 95 ]
689 x 2 = n x 106
n = 1378 / 106
n = 13
Therefore, the number of terms for the arithmetic series is 13.
To know more about arithmetic progression follow
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