Question 1187650
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If the first term is a and the common difference is d, then<br>
3rd term: a+2d
7th term: a+6d
21st term: a+20d<br>
The given information is<br>
[1] {{{a+6d = 25}}} (the 7th term is 25)
[2] {{{(a+2d)/a=(a+20d)/(a+2d)}}} (the 1st, 3rd, and 21st term form a geometric sequence)<br>
Working with [2] will give you an expression for d in terms of a; substituting the result into [1] will give you the answer.  I'll get you started; the rest is straightforward.<br>
{{{(a+2d)/a=(a+20d)/(a+2d)}}}
{{{(a+2d)^2=a(a+20d)}}}
{{{a^2+4ad+4d^2=a^2+20ad}}}
{{{4ad+4d^2=20ad}}}
{{{4d^2-16ad=0}}}
{{{4d(d-4a)=0}}}<br>
d=4a<br>
You can finish....<br>