Calculate: The first term of a linear sequence is 5 and the common difference is 3, find the 15th term of the sequence
By the time you finished typing this question, you should have been able to do the arithmetic mentally ....
term(15) = a + 14d
= 5 + 14(3)
= ..
The procedure is to long
T15=a+14d
=5+14(-3)
=5+-42
=-37
The nth term of a linear sequence is:
an = d ∙ n - c
where
d = common difference
c = constant that you´ll need to calculate
In this case:
a1 = 5 , d = 3 , n = 1
a1 = d ∙ n - c
5 = 3 ∙ 1 - c
5 = 3 - c
Subtract 3 to both sides
2 = - c
Multiply both sides by - 1
- 2 = c
c = - 2
So the nth term of your linear sequence is:
an = d ∙ n - c
an = 3 n - ( - 2 )
an = 3 n + 2
15th term of the sequence:
an = 3 n + 2
where n = 15
a15 = 3 ∙ 15 + 2
a15 = 45 + 2
a15 = 47