Answered

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

Sagot :

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

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