A linear sequence has a 3rd term = 7, and a 6th term = 36. What is the 8th term?
a+2d = 7
a+5d =36
subtract them:
3d = 29
d = 29/3
then a + 58/3 = 7
3a + 58 = 21
a = -37/3
term(8) = a + 7d
= -37/3 + 7(29/3) = 166/3
check:
-37/3 , -8/3 , 7 , 50/3 , 79/3 , 36, 137/3, 166/3, ..
notice every 3rd term would be a whole number
To find the 8th term of the linear sequence, we need to determine the common difference (d) of the sequence and then use it to calculate the 8th term.
The common difference (d) is the difference between any two consecutive terms in the sequence. One way to find the common difference is to subtract the 3rd term from the 6th term:
d = 6th term - 3rd term
= 36 - 7
= 29
Now that we know the common difference (d = 29), we can find the 8th term by adding this difference to the 6th term:
8th term = 6th term + 2d
= 36 + 2(29)
= 36 + 58
= 94
Therefore, the 8th term of the linear sequence is 94.