# If a, b, c, d, e, f are in A.P., then f – c is equal to:

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If a, b, c, d, e, f are in A.P., then f – c is equal to:
1. 2 (e - d)
2. 2 (c - a)
3. 3 (e - d)
4. e - a

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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.