Question

Write the first five terms of
$\sf a_n$ = (2n – 3)/6

Answer 1

$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• $\textsf{Write the first five terms of :-}$

• $\sf a_n$ = $\sf \dfrac{2n \: - \: 3}{6}$

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• $\textsf{The first five terms in the A.P will be,}$

• $\sf a_1$ , $\sf a_2$ , $\sf a_3$ , $\sf a_4$ , $\sf a_5$

• $\textsf{This means that n = 1,2,3,4,5 will be for the first five terms respectively.}$

• $\textsf{First term of A.P,}$

• $\textsf{Substituting n = 1,}$

• $\sf \dag \:\:\:\:\dfrac{2 \: * \: 1 \: - \: 3}{6} \: = \: \dfrac{- \: 1}{6}$

• $\textsf{Second term of A.P,}$

• $\textsf{Substituting n = 2,}$

• $\sf \dag \:\: \:\:\dfrac{2 \: * \: 2 \: - \: 3}{6} \: = \: \dfrac{1}{6}$

• $\textsf{Third term of A.P,}$

• $\textsf{Substituting n = 3,}$

• $\sf \dag \:\:\:\:\dfrac{2 \: * \: 3 \: - \: 3}{6} \: = \: \dfrac{3}{6} \: = \: \dfrac{1}{2}$

• $\textsf{Fourth term of A.P,}$

• $\textsf{Substituting n = 4,}$

• $\sf \dag \:\:\:\:\dfrac{2 \: * \: 4 \: - \: 3}{6} \: = \: \dfrac{5}{6}$

• $\textsf{Fifth term of A.P,}$

• $\textsf{Substituting n = 5,}$

• $\sf \dag \:\:\:\:\dfrac{2 \: * \: 5 \: - \: 3}{6} \: = \: \dfrac{7}{6}$

$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\therefore{\sf a_{1} \: = \: \dfrac{- \: 1}{6}}$

• $\therefore{\sf a_{2} \: = \: \dfrac{1}{6}}$

• $\therefore{\sf a_{3} \: = \: \dfrac{1}{2} \: or \: \dfrac{3}{6}}$

• $\therefore{\sf a_{4} \: = \: \dfrac{5}{6}}$

• $\therefore{\sf a_{5} \: = \: \dfrac{7}{6}}$

• $\boxed{\therefore{\sf A.P \: = \: \dfrac{- \: 1}{6} \: , \: \dfrac{1}{6} \: , \: \dfrac{3}{6} \: , \: \dfrac{5}{6} \: , \: \dfrac{7}{6}.}}$

Answer 2

Required answer:-

Question:

$•Write \: the \: first \: five \: terms \: of : a_{n} = (2n - 3)/6$

Solution:

Given,

$•a_{n} = (2n - 3)/6$

To find:

• first five terms of (2n -3)/6

Assumptions:

• Taking n as 1 , 2 , 3 , 4 , 5 , 6

Step by step explaination:

First term

✎Putting value...

$a_{1} = \frac{2 \times 1 - 3}{6} = \frac{ - 1}{6}$

Second term

✎Putting value...

$a_{2} = \frac{2 \times 2 - 3}{6} = \frac{1}{6}$

Third term

✎Putting value...

$a_{3} = \frac{2 \times 3 - 3}{6} = \frac{1}{2}$

Fourth term

✎Putting value....

$a_{4} = \frac{2 \times 4 - 3}{6} = \frac{5}{6}$

Fifth term

✎Putting value.....

$a_{5}= \frac{2 \times 5 - 3}{6} = \frac{7}{6}$

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Thus, the first five terms are :

$\frac{ - 1}{6} , \: \frac{1}{6} , \: \frac{1}{2}, \: \frac{5}{6} , \: \frac{7}{6}$

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