The 26th, 11th and the last term of an A.P. are 0, 3 and -1/5 respectively. Find the common difference and the number of terms for this question iam getting n= -25 .but ans shows n=27.

Question

if ans n=- 25 is it wrong explain me the whole process in this question

Answer 1

so we have; term a26=0 , term a11=3 and last term an=-0.2 ( -1/5 = -0.2)

let common difference is d  we have d=(a26-a11)/(26-11)  substituting the values we get;

(0-3)/(26-11)  -->>>  -3/15 = -0.2  so common difference d=-0.2

Now lets calculate the number of terms n ( it is obvious that we can not have a negative number of a term.

so we can not have n=-25 .  number of terms are possitive numbers)

so we have  an=a26+(n-26)(-0.2)   {the -0.2 is the common difference we have found before}

subsituting the values we have;  -0.2=0+(n-26)(-0.2)  -->>> -0.2=(n-26)(-0.2)

deviding by -0.2 both sides of the equation we get;  

1=n-26  solving for n we get;  n=26+1  so n=27

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