Question

the 11th term and 21st term of an A. P. are 16 and 29 respectively. Find first and common difference.

Answer 1

11th term of  the AP= 16=a+10d
21st term of the AP=29=a+20d

Solve both the equations

 a+10d=16
 a+20d=29
-  -       -
-10d= -13

Hence value of d= -13/-10
d=1.3
Put value of d in equation.
a+10(1.3)=16
a=16-13
a=3

Answer 2

11th Term = a+10d = 16 -----------(1)
21th Term = a + 20d= 29 -------(2)

By subtracting equation (1) from equation (2), we get ;
(a+20d) - (a+10d) = 29-16
10d = 13
d = 1.3

a = 16-(10×1.3)
a = 3

Therefore the respective first term and common difference of the given A.P is 3 & 1.3.



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