Question

the sixth term of an AP is 19 and iys seventeenth term is 41. find the 50th term of the AP

Answer 1

nth term of an AP

an = a1 + (n - 1)d

6th term is 19

19 = a + 5d -------------- [ 1 ]

17th term is 41

41 = a + 16d -------------- [ 2 ]

Find d:

[ 2 ] - [ 1 ]:

22 = 11d

d = 2

Find a1:

Sub d = 2 into [ 1 ]

19 = a1 + 5(2)

19 = a1 +10

a1 = 9

Find the nth term:

an = a1 + ( n - 1 )d

an =9 + (n - 1)2

an = 9 + 2n - 2

an = 7 + 2n

Find the 50th term:

an = 7 + 2n

a50 = 7 + 2(50)

a50 = 107

Answer: The 50th term is 107

Answer 2

Here is your answer OK

a6= 19
a+ 5d = 19 ______ 1
a17= 41
a +16d = 41 _____ 2
subtract 1 from 2 we get
d= 2
substituting d =2 in equation 1
a+5d = 19
a = 19- 5(2)
a= 9
we will get a = 9
now
a40= a + 39d
​ = 9 + 39(2)
= 87
therefore 40th term of A.P is 87