help me :)
- Thread starter mathe25
- Start date
find the first element(factor a1) and the arithmetic strig distance if :
a1+a2+a3=18 and a1*a2*a3=162
firs element is a1
arithmetic strig is an
distance is d
1. Replace \(\displaystyle a_2 = a_1 +d \) and \(\displaystyle a_3 = a_1 + 2d \).
Determine \(\displaystyle a_1\) wrt d from the 1st equation.
2. Use the same substituion with the 2nd equation. Plug in the term of a into the modified 2nd equation which yields an equation in d.
Determine d.
3. You'll get 2 different values for \(\displaystyle a_1\) and d.
whats means WRT and Plug in the term of a into the modified 2nd equation which yields an equation in d.
Determine d." "because iam from europe and i do not understad very well
1. Quite funny: I live in Europe too and I know that there are spoken at least 73.6 different languages. Which language are you used to use?
2. With an arithmetic sequence you know that:
\(\displaystyle a_2 = a_1 +d\)
and
\(\displaystyle a_3 = a_1+2d\)
Thus your 1st equation becomes:
\(\displaystyle a_1+a_1+d+a_1+2d=18~\implies~3a_1 + 3d =18~\implies~\boxed{a_1 = 6-d}\)
3. If you replace \(\displaystyle a_2\) and \(\displaystyle a_3\) in the 2nd equation you'll get:
\(\displaystyle a_1 \cdot (a_1+d) \cdot (a_1+2d)=162\)
Replace \(\displaystyle a_1\) by (6 - d):
\(\displaystyle (6-d) \cdot (6-d+d) \cdot (6-d+2d)=162~\implies~(6-d)(6+d)=27\)
Solve for d.