Correct Answer - Option 3 : 3 (e - d)
Concept:
nth term of an AP:
The formula for finding the nth term of an AP is:
an = a + (n - 1)d
Where, a = First term, d = Common difference, n = number of terms and an = nth term
Calculation:
Let x be the common difference of the AP a, b, c, d, e, f
We know that,
an = a + (n - 1)d
1st term, a = a
2nd term, b = a + x
3rd term, c = a + 2x
4th term, d = a + 3x
5th term, e = a + 4x
As f is the 6th term
f = a + (6 - 1)x
f = a + 5x ....(i)
c = a + 2x ....(ii)
Using equation (i) and (ii) we get,
f - c = a + 5x - a - 2x
f - c = 3x ....(iii)
Now we check through option,
suppose we take option 3 i.e.
3(e - d) = 3 (a + 4x - a - 3x) = 3x ....(iv)
So equation (iii) and (iv) are equal
Hence, the correct option is 3 as the other option doesn't satisfy.