# The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is a 1, what is an equation for the nth term of this sequence?

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The terms in the standard Arithmetic sequence are.

#a_1,a_1+d,a_1+2d,a_1+3d,.........,a_1+(n-1)d# where

#a_1" is the 1st term and d, the common difference"#

#a_1+(n-1)d" is the nth term"# To obtain the nth term formula , we require to find

#a_1" and d"# we are given:

#a_3=10" and " a_5=26#

#a_3=10rArra_1+2d=10rArra_1=10-2d.....(1)#

#a_5=26rArra_1+4d=26rArra_1=26-4d.......(2)# equating (1) and (2): 10 -2d = 26 - 4d → d = 8

substitute d = 8 in (1) :

#a_1=10-16=-6# We now have d = 8 and

#a_1=-6#

#rArra_n=-6+8(n-1)=8n-14#

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Equation for nth term is

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In this AP, the 3rd term is

In an AP

So by the formula:

where (d is common difference)

Similarly,

Solving these two equations by subtracting:

we get

Now put these values in the formula:

We get:

(Answer )

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