The sum of the first 5 terms of an arithmetic series is 85, and the sum of the first 6 terms is 123. Write the first 3 terms of the series.
Okay i tried, but ended up with strange numbers.
formulas:
tn=t1+(n-1)d
sn=n/2(2(t1)+(n-1)d)
please help
The sum of the first 5 terms of an arithmetic series is 85, and the sum of the first 6 terms is 123. Write the first 3 terms of the series.
Okay i tried, but ended up with strange numbers.
formulas:
tn=t1+(n-1)d
sn=n/2(2(t1)+(n-1)d)
please help
Using the summation formula, we find:
$\displaystyle S_5=\frac{5}{2}(2t_1+4d)=85$
$\displaystyle S_5=3(2t_1+5d)=123$
The two equations may be written:
$\displaystyle t_1+2d=17$
$\displaystyle 2t_1+5d=41$
Now, solve this system to determine $\displaystyle t_1$ and $\displaystyle d$.
answer is d=7 t1=3
I actually wrote it out exactly like you did, but then i got help from another site as well and the person said that i could bring the fraction (5/2 & 6/2) over and use it to divide with 85 and 123. whew. I made it seem so difficult lol.
I blame my teacher for not showing the proper steps!!!
Oh and the two equations with 17 and 41 confuses me, so i didn't know what to do with them.
Given the system:
(1) $\displaystyle t_1+2d=17$
(2) $\displaystyle 2t_1+5d=41$
I would multiply (1) by -2, then add the two equations to eliminate $\displaystyle t_1$:
$\displaystyle d=7$
and then using (1), we find:
$\displaystyle t_1=3$