Question

If a minus a minus b a + the a + 2d are in ap then the common difference will be

Answer 1

Answer:

A.P: a, a+d, a+2d …

Here, we first need to write the expression for an-ak

Now, as we know,

an=a+(n-1)d

So for the nth term

an=a+(n-1)d

Similarly for kth term

ak=a+(k-1)d

So,

an-ak=(a

= a + nd - d - a - kd + d

= nd - kd

= (n - k)d

So. a_n - a_k = (n - k)d

We are given, a_10 - a_5 = 200

Here

Let us take the first term as a and the common difference as d

Now, as we know,

a_n = a + (n -1)d

Here we find a_30 and a_20

So, for 10th term,

a_10 = a + (10 - 1)d

= a + (9)d

Also for 5 th term

a_5 = a + (5 - 1)d

= a + (4)c

So

a_10 - a_5 = (a +_ 9d)- (a + 4d)

200 = a + 9d - a - 4d

200 = 5d

d = 200/5

d = 40

Therefore the common difference for the A.P. is d = 40