The 18th term of Arithmetic progression is 99 and 29th term is 165. Find the first term and common difference

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

answer:     true

step-by-step explanation:

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.