Answer:
The difference between the given terms is
–73 – (–40) = –33.
The difference between the term numbers is 28 – 17 = 11.
Dividing –33 / 11 = –3.
The common difference is –3.
The recursive formula is the previous term minus 3, or an = an – 1 - 3 where a17 = -40
Step-by-step explanation:
The nth term of an arithmetic sequence is expressed as Tn = a + (n-1)d. The recursive formula for this sequence is Tn = 3Tn-1
The nth term of an arithmetic sequence is expressed as:
Tn = a + (n-1)d
where
a is the first term
n is the number of terms
d is the common difference
If the 17th term is -40 and the 28th term is -73 hence;
a + 16d = -40
a + 27d = -73
Subtract
16d - 27d = -40 + 73
-11d = -33
d = 3
The required recursive function is given as:
Tn = dTn-1
Tn = 3Tn-1
Hence the recursive formula for this sequence is Tn = 3Tn-1
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