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If the First, Second and Last Term of an A.P. Are A, B and 2a Respectively, Its Sum is - Mathematics

MCQ

If the first, second and last term of an A.P. are ab and 2a respectively, its sum is

Options

  • \[\frac{ab}{2(b - a)}\]

     

  • \[\frac{ab}{(b - a)}\]

     

  • \[\frac{3ab}{2(b - a)}\]

     

  •  none of these 

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Solution

In the given problem, we are given first, second and last term of an A.P. We need to find its sum.

So, here

First term = a

Second term (a2) = b

Last term (l) = 2a

Now, using the formula  an = a+ ( n - 1) d 

a2 = a + (2 - 1)d

  b = a + d 

  d = b - a                 ......(1) 

Also,

an = a + (n-1) d

 2a = a + nd - d 

2a - a = nd - d 

`(a + d)/d = n `                     ...........(2) 

Further as we know,

`S_n = n/2 [ a + l]`

Substituting (2) in the above equation, we get

Using (1), we get

`S_n = ( a + (b - a) )/(2(b - a)) (3a) `

`S_n =b / ( 2 ( b-a) ) (3a)`

Thus,

`S_n = (3ab)/(2(b-a))`

 

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Q 12 | Page 57
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