Question

Write the arithmetic progression when first term a and common difference of d are as follows:
(i)a=4,d=-3
(ii)a=-1,d=1/2
(iii)a=-1.5,d=-0.5

Answer 1

• When the first term and common difference is given then by using following formula further terms can be determined :                                                                          

        $a_{n}$ = $a_{n-1}$ + d

• where $a_{n-1}$ is the given term or first term

• d is common difference

• $a_{n}$ is the next term and n= 1, 2 ,3, 4, ...........

• (i) a = 4, d= -3 ,                                                                              then second term will =  4+(-3) = 1,                                          third term =1 + (-3) = -2,                                                            fourth term = -2 +(-3) = -5,                                                        fifth term = -5 + (-3) = 8,    and so on ....

• (ii) a = -1 , d= 1/2                                                                             second term = -1 + 1/2 = -1/2                                                   third term = -1/2 + 1/2 = 0                                                         fourth term = 0 + 1/2 = 1/2                                                       fifth term = 1/2 + 1/2 = 1,      and so on ....

• (iii)a = -1.5, d = -0.5                                                                         second term = -1.5 + (-0.5) = -2                                               third term = -2 + (-0.5) = -2.5                                               fourth term = -2.5 + (-0.5) = -3                                               fifth term = -3 + (-0.5) = -3.5,   and so on....

Answer 2

Given:-

1. a = 4 and d = - 3
2. a = 1 and d = 1/2
3. a = -1.5 and d = -0.5

To find :-

• aritjmetic progression witj first and common difference are follow

Solution:-

$1)a_{1} = 4 \\ \: \: \: d = - 3 \\ \\ for \: a.p \\ \\ a_{1} = 4 \\ \\ a_{2} = a_{1} + d = 4 + ( - 3) \\ \: \: \: \: = 4 - 3 = 1 \\ \\ a_{3} = a_{2} + d = 1 + ( - 3) \\ \: \: \: \: \: = 1 - 3 = - 2 \\ \\ a_{4} = a_{3} + d = - 2 + ( - 3) \\ \: \: \: \: \: = - 2 - 3 = - 5 \\ \\ a \: .p \\ 4 ,\: \: 1, \: - 2, \: - 5$

$2)a = 1 \\ \: \: \: d = \frac{1}{2} \\ \\ a_{1} = 1 \\ \\ a_{2} = a_{1} + d = 1 + \frac{1}{2} \\ \: \: \: \: \: = \frac{3}{2} \\ \\ a_{3} = a_{2} + d = \frac{3}{2} + \frac{1}{2} \\ \\ \: \: \: \: \: = \frac{4}{2} = 2 \\ \\ a_{4} = a_{3} + d = 2 + \frac{1}{2} \\ \\ \: \: \: \: \: \: \: \: = \frac{5}{2} \\ \\ a.p \: is \\ 1 ,\: \: \frac{3}{2} ,\: \: \: 2, \: \: \: \: \: \frac{5}{2},$

$a = - 1.5 \\ d = - 0.5 \\ \\ a_{1} = - 1.5 \\ \\ a_{2} = a_{1} + d = - 1.5 + ( - 0.5) \\ \: \: \: \: \: = - 2 \\ \\ a_{3} = a_{2} + d = - 2 + ( - 0.5) \\ \: \: \: \: \: = - 2.5 \\ \\ a_{4} = a_{3} + d = - 2.5 + ( - 0.5) \\ \: \: \: \: \: = - 3 \\ \\ a.p \: \: is \\ - 1.5 ,\: \: \: - 2 ,\: \: \: \: - 2.5, \: \: \: \: \: \: - 3$