Given that the first term of an a.p is 7 and it's 10th term is twice the second term find the 19th term
Let the common difference of the arithmetic progression be d.
The first term is 7, so the nth term can be represented as 7 + (n-1)d.
The 10th term is twice the second term, so we have the equation:
7 + 9d = 2(7 + d)
7 + 9d = 14 + 2d
9d - 2d = 14 - 7
7d = 7
d = 1
Now that we know the common difference is 1, we can find the 19th term:
19th term = 7 + (19-1)1
= 7 + 18
= 25
Therefore, the 19th term is 25.