Question

for an AP the 7th term is -1 and the 16th term is 17. find the general term of the AP

Answer 1

Let a be the first term and d be the common difference of the AP.
SO, it is given that 7th term=-1
therefore,
a + ( n-1 )d = -1
a + ( 7-1)d = -1
a + 6d = -1. ....(1)
And, 16th term=17
a + ( 16-1 )d = 17
a + 15d = 17. ......(2)
BY, subtracting (1) from (2), we get,
a +15d - a - 6d = 17 - (-1)
9d =18
d=2
THEREFORE, a= 17 - 15d
a= -13
THUS, general term of AP = a + ( n-1)d
= -13+ (n-1)2
= -13 +2n -2
= 2n-15
HENCE, GENERAL TERM OF AP= 2n-15