Question

The 9th term and the 21st term of an AP are 75 and 183 respectively.find the 81st term of the AP

Answer 1

a9= a+8d=75 >1 eq
a21=a+20d=183>2eq
a81=?
a+8d=75
a+20d=183
- - -
= -12d=- 108
- gets cancel
12d=108
d=108/12
d=9

substitute d in equation 1
a+8(9)=75
a+72=75
a=75-72
a=3

a81=a+80d
=3+80(9)
=3+720
=723

a81=723

Answer 2

Answer:

9th term = 75  

a + (n-1)d = 75

a + (9-1)d = 75

a + 8d = 75  

a = 75 - 8d --- (i)

21st term = 183

a + (n-1)d = 183

a + (21-1)d = 183

a + 20d = 183

a = 183 - 20d --- (ii)

75 - 8d = 183 - 20d  

20d - 8d = 183 - 75  

12d = 108  

d = 9

75 - 8d = a

75 - 8(9) = a

75 - 72 = a  

3 = a

81st term of AP:-

a + (n-1)d

3 + (81-1)9

3 + (80)9  

3 + 720  

723 Ans

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