# HOW TO FIND FIRST TERM AND COMMON DIFFERENCE FROM nth TERM

How to Find First Term and Common Difference from nth Term :

Here we are going to see how to find the first term and common difference from the nth term of the sequence.

Question 1 :

Find the first term and common difference of the Arithmetic Progressions whose nth terms are given below

(i) tn = −3 +2n

Solution :

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

 1st term t1 = −3 + 2(1) t1 = −3 + 2  =  -1 2nd term t2 = −3 + 2(2) t2 = −3 + 4  =  1

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

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

(ii) tn = 4 - 7n

Solution :

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

 1st term t1 =  4 - 7(1) t1 = 4 - 7  =  -3 2nd term t2 =  4 - 7(2) t2 = 4 - 14  =  -10

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

Solution :

nth 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 15th term of the given sequence is -54.

After having gone through the stuff given above, we hope that the students would have understood, "How to Find First Term and Common Difference from nth Term".

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