Question

Write the arithmetic progression when first term $a$ and common difference $d$ are as follows:
$a=-1;d=\frac{1}{2}$

Answer 1

Given, first term of the arithmetic progression is

$a=-1$

And common difference of A.P is

$d=\frac{1}{2}$

The nth term of an arithmetic progression is given by

$a_n=a+(n-1)d....eq\left(1\right)$

Hence first term $a_1$ by putting n=1 in eq(1)

$a_1=-1+(1-1)\frac{1}{2}$

$a_1=-1+\left(0\right)\frac{1}{2}$

$a_1=-1.......eq\left(2\right)$

Hence second term $a_2$ by putting n=2 in eq(1)

$a_2=-1+(2-1)\frac{1}{2}$

$a_2=-1+\frac{1}{2}$

$a_2=-\frac{1}{2}.......eq\left(3\right)$

Hence third term $a_3$ by putting n=3 in eq(1)

$a_3=-1+(3-1)\frac{1}{2}$

$a_3=-1+\left(2\right)\frac{1}{2}$

$a_3=-1+1$

$a_3=0.......eq\left(4\right)$

Hence fourth term $a_4$ by putting n=4 in eq(1)

$a_4=-1+(4-1)\frac{1}{2}$

$a_4=-1+\left(3\right)\frac{1}{2}$

$a_4=-1+\frac{3}{2}$

$a_4=\frac{1}{2}.......eq\left(5\right)$

and so on

$a_n=a+(n-1)d$

Hence the arithmetic progression is.

$-1,-\frac{1}{2},0,\frac{1}{2}$