Question

An arithmetic sequence may have a positive or negative difference. In each of the f a. " 9, 14, 19, 24, b. 4- 3x, 4-X, 4+x, a. The common difference is The next two terms in order are and b. The common difference is The next two terms in order are and

Answer 1

If $a_n$ and $a_{n+1}$ are the n^th and (n+1)^th term of an arithmetic sequence, then the difference 'd' will be

:$a_{n+1}-a_n=d$, or $a_{n+1}=a_n+d$

a)

The 1st term, that is $a_1=-9$ , and the second term $a_2=-14$

The difference  $d=a_2-a_1=-14-(-9)=-14+9=-5$

The fourth term is $a_4=-24$ .

The fifth term will be $a_5=a_4+d=-24-5=-29$

The sixth term will be $a_6=a_5+d=-29-5=-34$

Next two terms in order are '-29' and '-34'

b)

The 1st term, that is $a_1=4-3x$ and the second term $a_2=4-x$

The difference  $d=a_2-a_1=4-x-(4-3x)=4-x-4+3x=2x$

The third term is $a_3=4+x$

The fourth term will be $a_4=a_3+d=4+x+2x=4+3x$

The fifth term will be $a_5=a_4+d=4+3x+2x=4+5x$

Next two terms in order are