Given:
6th term of an A.P is 19 and 17th terms of an A.P. is 41
So, a6 = 19 and a17 = 41
We know, an = a + (n – 1) d [where a is first term or a1 and d is common difference and n is any natural number]
When n = 6:
a6 = a + (6 – 1) d
= a + 5d
Similarly, When n = 17:
a17 = a + (17 – 1)d
= a + 16d
According to question:
a6 = 19 and a17 = 41
a + 5d = 19 ……………… (i)
And a + 16d = 41………….. (ii)
Let us subtract equation (i) from (ii) we get,
a + 16d – (a + 5d) = 41 – 19
a + 16d – a – 5d = 22
11d = 22
d = 22/11
= 2
Put the value of d in equation (i):
a + 5(2) = 19
a + 10 = 19
a = 19 – 10
= 9
As, an = a + (n – 1)d
a40 = a + (40 – 1)d
= a + 39d
Now put the value of a = 9 and d = 2 in a40 we get,
a40 = 9 + 39(2)
= 9 + 78
= 87
Hence, 40th term of the given A.P. is 87.