Fill In The Blanks[1 Marks ]

Question 11 Mark

The third term of a G.P. is 4. The product of the first five terms is _____.

Answer

The third term of a G.P. is 4. The product of the first five terms is $4^5.$
Solution:
Let a and r the first term and common ratio, respectively.
Given that the third term is 4.
$\therefore\ \text{ar}^2=4$
Product of the first five terms $=\text{a}.\text{ar}.\text{ar}^2.\text{ar}^3.\text{ar}^4=\text{a}^5\text{r}^{10}=\big(\text{ar}^2\big)^5=4^5$

View full question & answer→

Question 21 Mark

For a, b, c to be in G.P. the value of $\frac{\text{a}-\text{b}}{\text{b}-\text{c}}$ is equal to _____.

Answer

For a, b, c to be in G.P. the value of $\frac{\text{a}-\text{b}}{\text{b}-\text{c}}$ is equal to $\frac{\text{a}}{\text{b}}\text{ or }\frac{\text{b}}{\text{c}}.$
Solution:
Since a, b and c are in G.P.
$\therefore\ \frac{\text{b}}{\text{a}}=\frac{\text{c}}{\text{b}}=\text{r}$ (constant)
$\Rightarrow\text{b = ar}$ and $\text{c = br}$
$\Rightarrow\text{c = ar . r = ar}^2$
So, $\frac{\text{a}-\text{b}}{\text{b}-\text{c}}=\frac{\text{a}-\text{ar}}{\text{ar}-\text{ar}^2}=\frac{\text{a}(1-\text{r})}{\text{ar}(1-\text{r})}=\frac{1}{\text{r}}=\frac{\text{a}}{\text{b}}=\frac{\text{b}}{\text{c}}$
Hence, the correct value of filler is $\frac{\text{a}}{\text{b}}\text{ or }\frac{\text{b}}{\text{c}}.$

View full question & answer→

Question 31 Mark

The sum of terms equidistant from the beginning and end in an $A.P.$ is equal to _____.

Answer

The sum of terms equidistant from the beginning and end in an $A.P. $is equal to first team $+$ last term.
Let $A.P$ be $a, a + d, a + 2d, a + 3d, …., a + (n - 1)d$
Taking first and last term
$a_1 + a_n = a + a + (n – 1)d = 2a + (n – 1)d$
Taking second and second last term
$a_2 + a_{n-2} = (a + d) + [a + (n - 2)d] = 2a + (n - 1)d = a_1 + a_n$
Taking third from the beginning and the third from the end
$a_3 + a_{n-2} = (a + 2d) + [a + (n - 3)d] = 2a + (n - 1)d = a_1 + a_n$
From the above pattern, we observe that the sum of terms equidistant from the beginning and the end in an $A.P$ is equal to the $[$first term $+$ last term$]$
Hence$,$ the correct value of the filler is first team $+$ last term.

View full question & answer→

Maths Fill In The Blanks[1 Marks ]

Take a timed test