PUMPA - SMART LEARNING

எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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A sequence is a function defined on the set of natural numbers $$\mathbb{N}$$. A sequence is a function of form $f:\mathrm{ℕ}\to \mathrm{ℝ}$, where $$\mathbb{R}$$ is the set of all real numbers.
If the sequence is of the form  $$a_1$$, $$a_2$$, $$a_3$$, $$a_4$$, ... then we can associate the function with the sequence $$a_1$$, $$a_2$$, $$a_3$$, $$a_4$$, ... by $$f (n) = a_n$$, $$n = 1, 2, 3,$$ …

Let us solve a problem of sequence with a function to understand this concept.
Example:
The general term for a sequence is defined as $f\left(n\right)={a}_{n}=\frac{3n+4}{n+6}$. Find the first three terms $$a_1$$, $$a_2$$, ${a}_{3}$.

Let us substitute the natural number $$n = 1, 2, 3, 4, ...$$ in the given equation.

The first three terms are:

$f\left(n\right)={a}_{n}=\frac{3n+4}{n+6}$, where $$n = 1, 2, 3, 4, ...$$

${a}_{1}=\frac{3\left(1\right)+4}{1+6}$

$=\frac{3+4}{7}$

${a}_{1}=\frac{7}{7}$

${a}_{2}=\frac{3\left(2\right)+4}{2+6}$

$=\frac{6+4}{8}$

${a}_{2}=\frac{10}{8}$

${a}_{3}=\frac{3\left(3\right)+4}{3+6}$

$=\frac{9+4}{9}$

${a}_{3}=\frac{13}{9}$

Therefore, the first three terms are $\frac{7}{7}$, $\frac{10}{8}$ and $\frac{13}{9}$.