# 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

#### 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?

#### APPEARS IN

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