Answer:
Given,
6th term of an A.P is 19 and 17th terms of an A.P. is 41
a6 = 19
a17 = 41
an = a + (n – 1) d
When n = 6,
a6 = a + (6 – 1) d
= a + 5d
When n = 17,
a17 = a + (17 – 1)d
= a + 16d
a6 = 19 and a17 = 41
a + 5d = 19 ……………… (i)
And a + 16d = 41………….. (ii)
Subtract equation (i) from (ii),
a + 16d – (a + 5d) = 41 – 19
a + 16d – a – 5d = 22
11d = 22
d = 22/11
d = 2
put the value of d in equation (i):
a + 5(2) = 19
a + 10 = 19
a = 19 – 10
a = 9
an = a + (n – 1)d
a40 = a + (40 – 1)d
= a + 39d
Now put the value of a = 9 and d = 2 in a40 ,
a40 = 9 + 39(2)
= 9 + 78
= 87
40th term of the given A.P. is 87.