If $\frac{1}{a + b}, \frac{1}{2 b}, \frac{1}{b + c}$ are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.

Q. If

\frac{1}{a + b}, \frac{1}{2 b}, \frac{1}{b + c}

are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.

Q. Let the

n^{t h}

terms of an A.P., G.P. and H.P. be

a, b, c

respectively. If the first and the

(2 n - 1)^{t h}

terms of the A.P., G.P. and H.P. are equal, then which of the following is/are correct?

Join BYJU'S Learning Program

Let a,b and c be the 7th,11th and 13th terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then ac is equal to:

The correct option is B 4a=A+6db=A+10dc=A+12da,b,c are in G.P⇒(A+10d)2=(A+6d)(A+12d)⇒Ad=−14⇒ac=A+6dA+12d=6+Ad12+Ad=6−1412−14=4

Let $a, b$ and $c$ be the $7 t h, 11 t h$ and $13 t h$ terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then $\frac{a}{c}$ is equal to: