Question

Obtain an arithmetic progression, where first term is - 3
& the common difference is 4.​

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given \: - \begin{cases} &\sf{An \: AP \: with \: first \: term \: = \: - 3 } \\ &\sf{common \: difference \: = \: 4} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: Find \: - \begin{cases} &\sf{An \: AP \: series}  \end{cases}\end{gathered}\end{gathered}$

Solution :-

Given

• First term of AP, a = - 3

• Common Difference of AP, d = 4

We know

Second term of series is

$\rm : \implies \:a_2 \: = \: a \: + \: d$

$\rm : \implies \:a_2 \: = \: - \: 3 \: + \: 4$

$\rm : \implies \boxed{ \pink{ \rm\:a_2 \: = \: 1}}$

Third term of series is

$\rm : \implies \:a_3 \: = \: a \: + \: 2d$

$\rm : \implies \:a_3 \: = \: - \: 3 \: + 2 \times 4$

$\rm : \implies \:a_3 = - 3 + 8$

$\rm : \implies \:\boxed{ \pink{ \rm\:a_3 \: = \: 5}}$

Fourth term of series is

$\rm : \implies \:a_4 \: = a \: + \: 3d$

$\rm : \implies \:a_4 \: = - 3 + 4 \times 3$

$\rm : \implies \:a_4 \: = - 3 + 12$

$\rm : \implies \:\boxed{ \pink{ \rm\:a_4 \: = \: 9}}$

So, required AP series is

$\boxed{ \pink{ \rm\: - \: 3, \:1, \: 5, \: 9,.. }}$