Answer:
The first term is -3 and the common difference is 6
Step-by-step explanation:
Recall that the nth term of an arithmetic progression AP is given as
Tn = a + (n - 1)d
where
Tn is the nth term
a is the first term and
d is the common difference while n is the number of terms
Given that the 18th term of Arithmetic progression is 99 and 29th term is 165 then
substituting the given values into the formula
a + 17d = 99
a + 28d = 165
solve both equations simultaneously
11d = 165 - 99
11d = 66
d = 66/11
= 6
recall that a + 17d = 99
a + 17(6) = 99
a + 102 = 99
a = 99 - 102
= -3
hence the first term is -3 and the common difference is 6
