Question

If the 7th term of a HP is 8, and the 8th term is 7 then its 15th term is

Answer 1

Answer:

$\frac{56}{15}$

Step-by-step explanation:

Let us assume that the H.P. is given by

$\frac{1}{a}, \frac{1}{a+d}. \frac{1}{a+2d},$,........ so on.

Now, the 7th term of this H.P. is =$\frac{1}{a+6d}=8$ {Given}.........(1)

Again, the 8th term of this H.P. is =$\frac{1}{a+7d}=7$ {Given}...... (2)

From the above two equations (1) and (2), we get

$(a+7d)-(a+6d)=\frac{1}{7}-\frac{1}{8}$

⇒ $d= (\frac{1}{7}-\frac{1}{8})=\frac{1}{56}$ ........ (3)

From equation (1), putting the value of d, we get,

$a+6*\frac{1}{56}=\frac{1}{8}$

⇒$a= \frac{7-6}{56}=\frac{1}{56}$ ........ (4)

Now, the 15th term of the H.P. is given by $\frac{1}{a+14d}$.

So, putting the values of a and d fro equatios (3) and (4)

$\frac{1}{a+14d}= \frac{1}{\frac{1}{56}+\frac{14}{56}}=\frac{1}{\frac{15}{56}}=\frac{56}{15}$

(Answer)