Find the arithmetic sequence: What is the 32nd term of the arithmetic sequence where a1 = 4 and a6 = 29 ? 155 159 163 167 

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Let a1, a2, a3, ....., an  be terms of arithmetic sequence.

Then, we will assume that the common difference is r.

Given that a1= 4   and a6 = 29

Then, we know that:

an = a1 + (n-1)*r

==> a6 = a1 + 5*r

Now we will substitute:

==> 29 = 4 + 5r

==> 5r = 25 ==> r= 5

Now let us calculate the terms a32.

==> a32= a1 + 31*r

==> a32 = 4 + 31*5 = 4 + 155 = 159

Then the answer is :

a32 = 159

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