“Superior Leaders Are Willing To Admit A Mistake And Cut Their Losses. Be Willing To Admit That You’ve Changed Your Mind. Don’t Persist When The Original Decision Turns Out To Be A Poor One.”

MISCELLANEOUS EXERCISE |

**Question 11. **A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

**Question 12. **The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms

**Question 13. **If \( \frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}(x \ne 0)\), then show that a, b, c and d are in G.P.

**Question 14. **Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that \(P^2R^n=S^n\)

**Question 15. **If *p*^{th}, *q*^{th} and *r*^{th} terms of an A.P. are *a*, *b*, *c*, respectively. Show that \((q-r)a+(r-p)b+(p-q)c=0\)

**Question 16. **If \( a \left ( \frac{1}{b}+\frac{1}{c} \right ) ,b \left ( \frac{1}{c}+\frac{1}{a} \right ), c \left ( \frac{1}{a}+\frac{1}{b} \right )\) are in A.P., prove that *a*, *b*, *c* are in A.P.

**Question 17. **If *a*, *b*, *c*, *d* are in G.P, prove that \((a^n+b^n),(b^n+c^n), (c^n+d^n)\) are in G.P.