Q1 of 167 Page 19

If are in A.P., prove that:
are in A.P.

We know, if a, b, c are in AP,

Then b - a = c - b

It is said that, are in AP,

Hence,

If are in AP, then

Taking LCM,

Now, LHS =

Multiply c in both numerator and denominator,

We get,

RHS

Multiply a in both numerator and denominator,

We get, =

Therefore, LHS = RHS

c(b - a) = a(b-c)

Also,

c(b - a) = a(b - c)

Hence given terms are in AP

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms

The sum of first n terms of two A.P.’s is in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.

If are in A.P., prove that:

a(b + c), b(c + a), c(a + b) are in A.P.

If a², b², c² are in A.P., prove that are in A.P.

If are in A.P., prove that:are in A.P.