# Arithmetic Progression

## Exercise 5.1 Part 2

Question: 2 – Write first four terms of AP, when the first term a and the common difference d are given as follows:

(i) a = 10, d = 10

Solution: Here, first term a1 = 10 and common difference, d = 10

Hence, second term a_2 = a_1 + d = 10 + 10 = 20

Third term a_3 = a_1 + 2d = 10 + 2 xx 10 = 30

Fourth term a_4 = a_1 + 3d = 10 + 30 = 40

Thus, first four terms of the AP will be 10, 20, 30, 40, ……

(ii) a = - 2, d = 0

Solution: First term a = 1

Common difference = 0

Thus, first four terms of given AP will be

a_1 = - 2, a_2 = - 2, a_3 = - 2 and a_4 = - 2

(iii) a = 4, d = - 3

Solution: Here, first term a1 = 4 and common difference d = - 3

We know that a_n = a + (n – 1)d, where n = number of terms

Thus, second term a_2 = a + (2 – 1)d

Or,a_2 = 4 + (2-1)xx (-3)

= 4 - 3 = 1

Similarly, third term a_3 = a + (3 – 1)d

a_3 = 4 + (3-1) xx (-3)

= 4 - 6 = -2

Fourth term a_4= a + (4-1)d

a_4 = 4 + (4 - 1) xx( -3)

= 4 - 9 = -5

Thus, the first four terms of given AP are; 4, 1, - 2, - 5

(iv) a = - 1, d = ½

Solution: Solution: We have, first term = - 1 and d = ½

a_2=a+(2-1)d
=-1+1/2=-1/2

a_3=a+2d
=-1+2xx1/2=0

a_4=a+3d
=-1+3xx1/2=1/2

Thus, the four terms are; - 1, -1/2, 0 and ½

(v) a = - 1.25, d = - 0.25

Solution: We have; first terms = - 1.25 and d = - 0.25

a_2= a + d

= -1.25 - 0.25 = -1.5

a_3 = a + 2d

= -1.25 + 2 xx (-0.25)

= -1.25 - 0.5 = -1.75

a_4 = a + 3d

= 1.25 + 3 × (-0.25) = -2.25

Thus, the first four terms are; - 1.25, -1.5, -1.75 and – 2.25

Question: 3 – For the following APs, write the first term and common difference,

(i) 3, 1, -1, - 3, …….

Solution: Here, first term a = 3

Common difference can be calculated as follows:

a_4 – a_3 = - 3 – ( -1) = - 3 + 1 = - 2

a_3 – a_2 = - 1 – 1 = - 2

a_2 – a_1 = 1 – 3 = - 2

Here, a(k+1) – a_k = - 2 for all values of k

Hence, first term = 3 and common difference = - 2

(ii) – 5, - 1, 3, 7

Solution: a_4 – a_3 = 7 – 3 = 4

a_3 – a_2 = 3 – (-1) = 3 + 1 = 4

a_2 – a_1 = - 1 – (-5) = - 1 + 5 = 5

Here, a_(k+1) – a_k = - 2 for all values of k

Hence, first term = - 5 and common difference = 4

Question (iii): 1/3, 5/3, 9/3, (13)/(3), ------

Solution:

a_4-a_3=(13)/(3)-9/3=4/3

a_3-a_2=9/3-5/3=4/3

a_2-a_1=5/3-1/3=4/3

Here, a_(k+1) – a_k = - 2 for all values of k

Hence, first term = 1/3 and common difference = 4/3

(iv) 0.6, 1.7, 2.8, 3.9, …….

Solution: a_4 – a_3 = 3.9 – 2.8 = 1.1

a_3 – a_2 = 2.8 – 1.7 = 1.1

a_2 – a_1 = 1.7 – 0.6 = 1.1

Here, a_(k+1) – a_k = - 2 for all values of k

Hence, first term = 0.6 and common difference = 1.1