Question

the 10th term of an A.P. is 31 and 20th term is 71. find its 30th term

Answer 1

10th term = 31
a + 9d = 31
a = 31 - 9d -----1equation

20th term = 71
a + 19d = 71
a = 71 - 19d

From 1equation,

31 - 9d = 71 - 19d
19d - 9d = 71 - 31
10d = 40
$d = \frac{40}{10}$

d = 4

Putting the value of d in 1equation,

a = 31 - 9d
a = 31 - 9(4)
a = 31 - 36
a = -5

Now,

30th term = a + 29(d)

30th term = -5 + 29(4)

30th term = -5 + 116

30th term = 111

I hope this will help you

(-:

Answer 2

Let a be the 1st term of the AP and d be the common difference
According to the question
a+(10-1)d=31
a+9d=31 --->(i)
a+19d=71 --->(ii)
ii-i
10d=40
d=4
Putting value of d in i
a+9*4=31
a+36=31
a=-5
30th term of the AP=a+(30-1)d
=-5+29*4=116-5
=111