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(D) To check if the sequence $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots$ is an $A.P.$,we calculate the difference between consecutive

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(D) To check if the sequence $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots$ is an $A.P.$,we calculate the difference between consecutive terms.Let $a_1 = \frac{1}{2}$,$a_2 = \frac{2}{3}$,$a_3 = \frac{3}{4}$,$a_4 = \frac{4}{5}$.Calculate the common difference $d_1 = a_2 - a_1 = \frac{2}{3} - \frac{1}{2} = \frac{4-3}{6} = \frac{1}{6}$.Calculate the common difference $d_2 = a_3 - a_2 = \frac{3}{4} - \frac{2}{3} = \frac{9-8}{12} = \frac{1}{12}$.Since $d_1 
eq d_2$,the difference between consecutive terms is not constant.Therefore,the given sequence is not an $A.P.$

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots$

Similar Questions

For an $A.P.$,the $3^{rd}$ term is $7$ and the $7^{th}$ term exceeds thrice the $3^{rd}$ term by $2$. Find the sum of first $20$ terms of the $A.P.$

Find the sum:
$1+(-2)+(-5)+(-8)+\ldots+(-236)$

For an $A.P.$,the $2^{nd}$ term is $2$ and the $7^{th}$ term is $22$. Find the sum of the first $30$ terms of the $A.P.$

The $n^{th}$ term of the $A.P.$ $5, 10, 15, 20, \ldots$ is....... (in $n$)

The sum of $n$ terms of an $A.P.$ is given by $S_{n} = 2n^{2} + 5n$. Then,the $n^{th}$ term of the $A.P.$ $T_{n} = \dots$

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