29
The third term of a GP is 4 , the product of the first five terms is ............. .
Explanation
It is given that, $T_3=4$
Let $a$ and $r$ the first term and common ration, respectively.
$$\begin{aligned} \text{Then, }\quad a r^2 & =4 \quad \text{.... (i)}\\ & \text { Product of first } 5 \text { terms }=a r \cdot a r \cdot a r^2 \cdot a r^3 \cdot a r^4\\ & =a^5 r^{10}=\left(a r^2\right)^5=(4)^5\quad \text{[using Eq. (i)]} \end{aligned}$$
30
Two sequences cannot be in both AP and GP together.
A
TRUE
B
FALSE
31
Every progression is a sequence but the converse, i.e., every sequence is also a progression need not necessarily be true.
A
TRUE
B
FALSE
32
Any term of an AP (except first) is equal to half the sum of terms which are equidistant from it.
A
TRUE
B
FALSE
33
The sum or difference of two GP, is again a GP.
A
TRUE
B
FALSE