Ques . If the first , second and last terms of AP are a , b and 2a respectively . Then its sum is
A) ab/2(b-a)
B) ab/( b-a)
C) 3ab / 2 (b-a)
D) None of these
Complete solution ✔✔✔✔✔
not just options otherwise reported ❎❎❎❎❎❎❎❎❎❎❎❎
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Answers
Answered by
7
Here,
a1 = a
a2 = b
common difference d = a2- a1 =
= b-a
let n be the number of terms in series
an = 2a = a + (n-1)d
(n-1) = a /(b-a)
n = (a/(b-a)) + 1
n= b/(b-a)
: sum = n/2 ( a1 +an)
= [b/2(b-a)] (a + 2a)
= 3ab/2(b-a)
So option c is the answer
Thanks!!!
Anonymous:
HI GM ♥️
Answered by
16
Let the AP series be x, x+d, x+2d…x+(n-1)d, where;
x is the first term of the sequence;
d is the arithmetic difference;
n is the number of terms.
According to the question;
first term=x=a;……(1)
second term=x+d=b;
d=b-a;……………….(2)
last term=x+(n-1)d=2a;
Substituting the value of d from equation 2 in the above equation, we get;
(n-1)(b-a)=a;
n-1=a/(b-a);
n=b/(b-a)…………..(3);
Hence as we know sum of terms of an AP=n/2[2*first term+(n-1)d];
Sum=b/2(b-a)[2a+a/(b-a)(b-a)];
sum=3ab/2(b-a). ANS
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