Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. $($ Assume that $n$ begins with $1)$ .
$1, \frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \frac{1}{9}, . . .$ then $a_{n} =______$

Open in App

Solution

Calculate the formula of $a_{n} .$
Given that the sequence is:
$1, \frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \frac{1}{9}, . . .$
It can be observed that for every $n^{th}$ term, the numerator is the same i.e $1$ and the denominator is an odd number in a sequence.
An odd number can be expressed as $2 n - 1$ .
Thus, the formula will be: $a_{n} = \frac{1}{2 n - 1}$ .
Where, $a$ is the collection of elements, $n$ is the term of the number.
Hence, the general term of the sequence is $\frac{1}{2 n - 1} .$

Suggest Corrections

Similar questions

Simplify $:$ $($ $\frac{3}{4}$ $\div$ $\frac{1}{2}$ $-$ $\frac{1}{3}$ $)$ $\times$ $\frac{6}{7}$

Simplify $:$ $\frac{3}{4}$ $\div$ $($ $\frac{1}{6}$ $\div$ $\frac{1}{2}$ $)$

Simplify $:$ $($ $\frac{2}{7}$ $+$ $\frac{1}{5}$ $)$ $\div$ $\frac{2}{21}$ of $($ $\frac{5}{7}$ $-$ $\frac{1}{3}$ $)$

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) $- 5, \frac{10}{3}, \frac{- 20}{9}, \frac{40}{27}, \frac{- 80}{81}, . . .$

Q. Consider the sequence

a_{n}

given by

a_{1} = \frac{1}{2}, a_{n} + 1 = a_{n}^{2} + a_{n}

Let

S_{n} = \frac{1}{a_{1} + 1} + \frac{1}{a_{2} + 1} + . . . . . . . . . . . + \frac{1}{a_{n} + 1}

then find the value of

[S_{2012}]

, where [.] denotes greatest integer function.

Join BYJU'S Learning Program

Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1).1,13,15,17,19,... then an=______

Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues. $($ Assume that $n$ begins with $1)$ .
$1, \frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \frac{1}{9}, . . .$ then $a_{n} =______$