Question

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

Answer 1

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

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

Answer 2

Just took the test. The answer is definitely A.