Question

If the $n^{th}$ term of an arithmetic progression is$(5n-2)$.

Find its first term, common difference and ${19}^{th}$ term.

Answer 1

Find the first term , common difference and ${19}^{th}$ term of the A.P

Given:

$n^{th}$ term $\left(Tn\right)=5n–2$

Step $1$:-

Put values for $n$:-

First term,$\left(T_1\right)=5\times 1–2=3$

Second term, $\left(T_2\right)=5\times 2–2=8$

Step $2$:-

Common Difference:-The common difference is the value between each successive number in an arithmetic sequence.

Therefore, the formula to find the common difference of an arithmetic sequence is: $d=a\left(n\right)-a(n-1)$, where $a\left(n\right)$is $n^{th}$term in the sequence, and $a(n-1)$is the previous term (or ${(n-1)}^{th}$ term) in the sequence.

Now,

Common difference(d) $=T_2-T_1$

$$\begin{gathered} =8-3 \\ =5 \end{gathered}$$

Step $3$:-

${19}^{th}$ term $\left(T_{19}\right):$

$\begin{array}{rcl}{T}_{{}_{19}}& =& a+\left(n-1\right)d\\ & =& 3+\left(19-1\right)5\\ & =& 3+18\times 5\\ & =& 3+90\\ & =& 93\end{array}$

$T_{19}=93$

Hence, If the $n^{th}$ term of an arithmetic progression is$(5n-2)$ then its first term $\left(T_1\right)is3$, common difference(d) is $5$ and ${19}^{th}$ term is $93$.