Question

The seventh term of an arithmetic sequence is 21, and the tenth term is 126. The first term is _____.

Answer 1

-189??

Answer 2

yes that is right! :)

Answer 3

Like this is how I would look at it:
we have these numbers:
\[a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,a_9,a_{10}\]
And
a_7=21
a_10=126
so we have
\[a_1,a_2,a_3,a_4,a_5,a_6,21,a_8,a_9,126\]
\[21-6x,21-5x,21-4x,21-3x,21-2x,21-x,21,21+x,21+2x,21+3x=126\]
So we can solve that last equation for x

Answer 4

21+3x=126
x=105/3=35
And then take that number and plug into the first term