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EastWind [94]
3 years ago
13

Find an equation for the nth term of the arithmetic sequence. a15 = -53, a16 = -5

Mathematics
2 answers:
lesantik [10]3 years ago
5 0
48n-773 is the equation for the nth term
ddd [48]3 years ago
3 0

Answer:  The required equation for the n-th term is a_n=-773+48n.

Step-by-step explanation:  We are given to find the equation for the nth term of the arithmetic sequence with the fifteenth and sixteenth term as follows :

a_{15}=-53,~~~a_{16}=-5.

We know that

the nth term of an arithmetic sequence with first term a and common difference d is given by

a_n=a+(n-1)d.

So, we have

a_{15}=-53\\\\\Rightarrow a+(15-1)d=-53\\\\\Rightarrow a+14d=-53~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

and

a_{16}=-5\\\\\Rightarrow a+(16-1)d=-5\\\\\Rightarrow a+15d=-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

Subtracting equation (i) from equation (ii), we get

(a+15d)+(a+14d)=-5-(-53)\\\\\Rightarrow d=48.

And, from equation (i), we get

a+14\times48=-53\\\\\Rightarrow a+672-53\\\\\Rightarrow a=-725.

Therefore, the n-th term of the given sequence is

a_n=a+(n-1)d\\\\\Rightarrow a_n=-725+(n-1)48\\\\\Rightarrow a_n=-773+48n.

Thus, the required equation for the n-th term is a_n=-773+48n.

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