Question

Find the common difference and ${15}^{th}$ term of the A.P. $125,120,115,110,$ ______

Answer 1

The given arithmetic progression is $125,120,115,110,......$ where the first term is $a_1=125$, second term is $a_2=120$ and so on.

We find the common difference $d$ by subtracting the first term from the second term as shown below:

$d=a_2-a_1=120-125=-5$

We know that the general term of an arithmetic progression with first term $a$ and common difference $d$ is $T_n=a+(n-1)d$

To find the ${15}^{15}$ term of the A.P, substitute $n=15,a=125$ and $d=-5$ in $T_n=a+(n-1)d$ as follows:

$T_{15}=125+(15-1)(-5)=125+(14\times (-5\left)\right)=125-70=55$

Hence, the $15$th term of the given A.P is $55$.