Home
Class 12
MATHS
If a(1),a(2),a(3),a(4) and a(5) are in A...

If `a_(1),a_(2),a_(3),a_(4)` and `a_(5)` are in AP with common difference `ne 0,` find the value of `sum_(i=1)^(5)a_(i) " when " a_(3)=2`.

Text Solution

Verified by Experts

`therefore a_(1),a_(2),a_(3),a_(4)and a_(5)` are in AP, we have
`a_(1)+a_(5)=a_(2)+a_(4)+ a_(3)+a_(3) " "[thereforet_(n)+t'_(n)=a+l]`
`a_(1)+a_(5)=a_(2)+a_(4)=4" "[therefore a_(3)=2]`
`a_(1)+a_(2)+a_(3)+a_(4)+a_(5)=4+2+4=10`
`implies " "sum_(i=1)^(5)a_(i)=10`
Promotional Banner

Similar Questions

Explore conceptually related problems

If a_(1), a_(2), a_(3).,,,,,,,,a_(n) are in A.P and their common difference is d. The value of the series sin d_(1) [sec a_(1).sec a_(2) + sec a_(2).sec a_(3)+ ….+ sec a_(n-1).sec a_(n)] is……..

If a_(1),a_(2),a_(3),...,a_(n) is an arithmetic progression with common difference d, then evaluate the following expression. tan[tan^(-1)(d/(1+a_(1)a_(2)))+tan^(-1)(d/(1+a_(2)a_(3)))+...+tan^(-1)(d/(1+a_(n-1)*a_(n)))]

If a_(1),a_(2),a_(3),"........" is an arithmetic progression with common difference 1 and a_(1)+a_(2)+a_(3)+"..."+a_(98)=137 , then find the value of a_(2)+a_(4)+a_(6)+"..."+a_(98) .

If a_(1),a_(2),a_(3),"….",a_(n) are in AP, where a_(i)gt0 for all I, the value of (1)/(sqrta_(1)+sqrta_(2))+(1)/(sqrta_(2)+sqrta_(3))+"....."+(1)/(sqrta_(n-1)+sqrta_(n)) is

A person is to count 4500 currency notes. Let a_(n) denotes the number of notes he counts in the nth minute. If a_(1)=a_(2)="........"=a_(10)=150" and "a_(10),a_(11),"......", are in AP with common difference -2 , then the time taken by him to count all notes is

If a_(1),a_(2),a_(3)(a_(1)gt0) are three successive terms of a GP with common ratio r, the value of r for which a_(3)gt4a_(2)-3a_(1) holds is given by

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

If a_(1), a_(2), a_(3),……,a_(n) are in AP, where a_(i) gt 0 for all i, show that (1)/(sqrt(a_(1)) + sqrt(a_(2))) + (1)/(sqrt(a_(2)) + sqrt(a_(3))) + …..+ (1)/(sqrt(a_(n-1))+ sqrt(a_(n)))= (n-1)/(sqrt(a_(1)) + sqrt(a_(n)))

Let b_(i)gt1" for "i=1,2,"......",101 . Suppose log_(e)b_(1),log_(e)b_(2),log_(e)b_(3),"........"log_(e)b_(101) are in Arithmetic Progression (AP) with the common difference log_(e)2 . Suppose a_(1),a_(2),a_(3),"........"a_(101) are in AP. Such that, a_(1)=b_(1) and a_(51)=b_(51) . If t=b_(1)+b_(2)+"........."+b_(51)" and " s=a_(1)+a_(2)+"........."+a_(51) , then

Statement I: If a=2hati+hatk,b=3hatj+4hatk and c=lamda a+mub are coplanar, then c=4a-b . Statement II: A set vector a_(1),a_(2),a_(3), . . ,a_(n) is said to be linearly independent, if every relation of the form l_(1)a_(1)+l_(2)a_(2)+l_(3)a_(3)+ . . .+l_(n)a_(n)=0 implies that l_(1)=l_(2)=l_(3)= . . .=l_(n)=0 (scalar).