4. Write a recursive formula for the sequence 7, 4, 1, –2, –5, .... Then find the next term
4 = 7 - 3
1 = 4 - 3
- 2 = 1 - 3
- 5 = - 2 - 3
This is arithmetic proggresion.
n-th member of A.P is:
an = a1 + ( n - 1 ) d
where a1 is first term , d is common difference
In this case:
a1 = 7 , d = - 3
an = a1 + ( n - 1 ) d
an = 7 + ( n - 1 ) • ( - 3 )
an = 7 - 3 n + 3
an = - 3 n + 10
Next term is a6 so n = 6
an = - 3 n + 10
a6 = - 3 • 6 + 10 = - 18 + 10
a6 = - 8
each term is 3 less than the previous term
a_1 = 7
a_n = a_(n-1) - 3
lol three tutors in one thread....
To write a recursive formula for a sequence, we need to find a pattern in the terms that allows us to express each term in terms of the previous term(s).
Looking at the given sequence, we can observe that each term is obtained by subtracting 3 from the previous term. The common difference between each term is -3. So, we can express the recursive formula as:
a(n) = a(n-1) - 3
where "a(n)" represents the nth term of the sequence and "a(n-1)" represents the previous term.
To find the next term in the sequence, we substitute the value of "n" by the next position, which is "6" since we are given 5 terms in the sequence.
a(6) = a(6-1) - 3
a(6) = a(5) - 3
Now, to find the value of a(5), we use the same formula:
a(5) = a(5-1) - 3
a(5) = a(4) - 3
And continue this process until we reach a(1):
a(4) = a(4-1) - 3
a(4) = a(3) - 3
a(3) = a(3-1) - 3
a(3) = a(2) - 3
a(2) = a(2-1) - 3
a(2) = a(1) - 3
Now, let's substitute the known values:
a(2) = 4 - 3
a(3) = 1 - 3
a(4) = -2 - 3
a(5) = -5 - 3
Continuing this process:
a(6) = -8 - 3
After evaluating the final expression, we find that the next term in the sequence is -11.
Therefore, the next term in the sequence is -11.