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Algebra
Question

(a) State the first term and common difference of...

(a) State the first term and common difference of the AP \(23,35,47 , \ldots\)

(b) Use the formula \(T _ { n } = a + ( n - 1 ) d\) to find the \(20\) th term and the \(600\) th term.

(c) Show that the formula for the \(n\) th term is \(T _ { n } = 11 + 12 n\) .

(d) Hence find whether \(143\) and \(173\) are terms of the sequence. (e) Hence find the first term greater than \(1000\) and the last term less than \(2000\) . (f) Hence find how many terms there are between \(1000\) and \(2000\) .

Answer

\(\left. \begin{array} { l } { \text { 5(a) } a = 23 , d = 12 \quad \text { (b) } T _ { 20 } = 251 , T _ { 600 } = 7211 } \\ { \left. \begin{array} { l l l } { \text { (d) } 143 = T _ { 11 } , 173 \text { is not a term. } } & { \text { (e) } T _ { 83 } = 2007 } \\ { T _ { 165 } = 1991 } & { \text { (f) } 83 \text { (Count both } T _ { 83 } \text { and } T _ { 165 } \text { . } } \end{array} \right. } \end{array} \right.\)

Solution
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