FIRST TERM AND COMMON DIFFERENCE OF AN ARITHMETIC SEQUENCE

Question 1 :

Find the first term and common difference of the arithmetic sequences whose n^th terms are given below

(i) t_n = -3 +2n

Solution :

To find the 1^st term of the sequence, we have to apply n = 1.

d = t₂ -  t₁   = 1 - (-1)  =  1 + 1  ==> d  =  2

Hence the first term and common difference are -1 and 2 respectively.

(ii) t_n = 4 - 7n

Solution :

To find the 1^st term of the sequence, we have to apply n = 1.

d = t₂ -  t₁   = -10 - (-3)  =  -10 + 3  ==> d  =  -7

Hence the first term and common difference are -3 and -7 respectively.

Question 2 :

Find the 19^th term of an A.P. -11,-15,-19,...

Solution :

n^th term of the A.P

tn  =  a + (n - 1)d

a = -11 , d = -15 - (-11)  =  -15 + 11  ==>  -4

t₁₉  =  -11 + (19 - 1)(-4)

=  -11 + 18(-4)

=  - 11 - 72

t₁₉  =   -83

Question 3 :

Which term of an A.P. 16, 11, 6, 1,... is -54 ?

Solution :

Let -54 be the nth term  of the sequence

tn  =  -54

a + (n - 1)d  =  -54

a  =  16 , d = 11 - 16  ==>  -5

16 + (n - 1)(-5)  =  -54

(n - 1)(-5)  =  -54 - 16

 (n - 1)(-5)  =  -70

 n - 1  =  -70/(-5)  ==>  14

n  =  14 + 1 

n  =  15

Hence 15^th term of the given sequence is -54.

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