The Eighth term is 75 and the 20th term is 39
A.)Find the first term and the common difference

Question

The Eighth term is 75 and the 20th term is 39
A.)Find the first term and the common difference

raden · Answer

use the formula :
a_n = a1 + (n-1)d

a8 = 75 -----> a1 + 7d = 75
a20 = 39 ----> a1 + 19d = 39

from both equation above, you can eliminate d, to get a1

anonymous · Answer

how exactly is "d" eliminated?

whpalmer4 · Answer

you've got two equations:
$$a_1 + 7d = 75$$$$a_1 + 19d = 39$$--------------

subtract down the columns and you'll get an equation involving only $d$.  Solve it.  Then plug the value you found back into either of the equations to solve for $a_1$.  Done.

whpalmer4 · Answer

You could also eliminate $d$ first, but that would require an extra step of multiplying one or both equations by a factor so that the $d$ "column" has equal coefficients like the $a_1$ column already has...

anonymous · Answer

so like a sytem of equations?

whpalmer4 · Answer

Yes, that's exactly what you're doing — solving a system of two equations in two unknowns.

anonymous · Answer

sweet, thanks alot

whpalmer4 · Answer

you're welcome!