Question

if sum of series 26 + 21 + 16... + x is equal to 11 thenfind the value of x ​

Answer 1

Given;

a=26 , d= - 5

Sum of n terms =11

Solution;

Sn = n/2[2a+(n-1)d]

11 = n/2[52+(n-1)×-5]

11 = n/2[52-5n+5]

11 = n/2[57-5n]

22 = n(57-5n)

22 = 57n-5n²

5n²-57n+22=0

5n²-55n-2n+22=0

5n(n-11) -2(n-11)=0

(5n-2)(n-11)=0

n=11,2/5

2/5 not possible so n=11

Sn =n/2(a+l)

11=11/2(26+l)

l=-24

Therefore the value of x is - 24.

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