Question

Find the 31st term of an A.P

whose 11th term is 38 and 6th term is 73

Answer 1

Ahoy,

11th term = a + 10d = 38......(i)

6th term = a + 5d = 73 ...(ii)

Substracting eq (ii) from (i) we get,

5d = -35

d = -7

a+10d = 38

=> a + 10×(-7) = 38

=> a-70= 38

=>a = 38+70
=> a = 108

31st term = a+30d

=> 108+30×-7

=>108-210

=>-102

Answer 2

Let a,d first term and common difference of given A. P
Then, a+10d=38 -(1)
a+5d=73 -(2)
subtracting 1 from 2 we get,
d= 35/ -5=-5
putting the value of d in 2 we get,
a=73+25=98
the required 31th term = 98+30×5=98+150=240.