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Find an equation for the nth term of the arithmetic sequence.

a10 = 32, a12 = 106

2 Answers

4 votes
an= -301+37(n-1) is the answer
User AeroBuffalo
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7 votes

Answer:

The nth for the arithmetic sequence is given by:


a_n=a+(n-1)d ....[1]

where,

a is the first term

d is the common difference of two consecutive terms.

n is the number of terms.

As per the statement:


a_(10) = 32 and
a_(12) =106

Using [1] we have;


a_(10) = a+9d


a+9d = 32 ......[2]


a_(12) =a+11d


a+11d =106 .......[3]

Subtract equation [2] from [3] we have;


a+11d-a-9d = 106-32

Simplify:


2d = 74

Divide both sides by 2 we get;

d = 37

Substitute the value of d in [2] we have;

a+9(37) = 32

a+333 = 32

Subtract 333 from both sides we have;

a = -301

Then substitute the value a and d in [1] we have;


a_n=-301+(n-1)(37)


a_n = -301+37n-37 = -338+37n

Therefore, an equation for the nth term of the arithmetic sequence is :


a_n = -338+37n

User Monkeyjumps
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