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Lynna [10]
4 years ago
9

In an arithmetic sequence, a14=-75 and a26=-123 Which recursive formula defines the sequence?

Mathematics
2 answers:
In-s [12.5K]4 years ago
7 0

Answer:

a_n=a_{n-1}-4,a_1=-23

A is the correct option.

Step-by-step explanation:

We have been given that a_{14}=-75,a_{26}=-123

The general term of an arithmetic sequence is given by

a_n=a+(n-1)d

Now, for 14th term,

a_{14}=a+(14-1)d\\a+13d=-75.....(1)

Similarly, for 26th term

a_{26}=a+(26-1)d\\a+25d=-123.....(1)

Subtract equation 1 and 2

-12d=48\\d=-4

From equation 1

a-52=-75\\a=-23

Hence, the first term is a_1=-23

Now, since the common difference d is -4.

Hence, the recursive formula is

a_n=a_{n-1}-4,a_1=-23

dimulka [17.4K]4 years ago
3 0

Just took the test. The answer is definitely A.

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