Arithmetic Sequences
Equation for Arithmetic Sequences
\[U_{n}=a+(n-1)d\]
Find the nth term of [40, 35, 30, 25
- \(a=40\)
- \(d=-5\)
- \(U_{n}=40+(n-1)(-5)\)
- \(U_{n}=40-5n+5\)
- \(U_{n}=45-5n\)
Exercise 3a:1
- \(a=7\), \(d=5\)
- \(a=7\), \(d=-2\)
- \(a=7.5\), \(d=0.5\)
- \(a=-9\), \(d=1\)
Exercise 3a:2
- nth term: \(2n+3\), 10th term :\(23\)
- nth term: \(3n+2\), 10th term: \(32\)
- nth term: \(-3n+27\), 10th term: \(-3\)
- nth term: \(4n-5\), 10th term: \(35\)
- nth term: \(xn\), 10th term: \(10x\)
- nth term: \(a+(n-1)d\), 10th term: \(a+9d\)
Exercise 3a:3
- \(22\) terms
- \(40\) terms
- \(39\) terms
- \(46\) terms
Exercise 3a:4
- \(a=14\)
- \(a+3d=32\)
- \(14+3d=32\)
- \(d=6\)
Exercise 3a:5
- \(q+5p=9\)
- \(q+8p=11\)
- \(3p=2\)
- \(p=\frac{2}{3}\)
- \(q=9-\frac{10}{3}\)
- \(q=\frac{17}{3}\)
Exercise 3a:6
- \(a+2d=30\)
- \(a+8d=9\)
- \(6d=21\)
- \(d=3.5\)
- \(a=23\)
- \(23+3.5n-3.5<0\)
- \(19.5<-3.5n\)
- \(n=6\)
- \(19.5-21=-1.5\)
- First negative term is \(-1.5\)