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Answer :
(i) 7, 13, 19 …, 205
First term = a = 7,
Common difference = d
= 13 – 7 = 19 – 13 = 6
And \(a_n = 205\)
Using formula \(a_n = a + (n - 1)d\) , to find nth term of arithmetic progression,
\(\Rightarrow \) 205 = 7 + (n - 1) 6 = 7 + 6n – 6
\(\Rightarrow \) 205 = 6n + 1
\(\Rightarrow \) 204 = 6n
\(\Rightarrow \) n = 34
Therefore, there are 34 terms in the given arithmetic progression.
(ii) 18, \({15}{\dfrac{1}{2}}\) , 13 …, -47
First term = a =18,
Common difference = d
= \({15}{\dfrac{1}{2}} - 18 \)
\( = {{31} \over {2}} - 18 \)
\( = {{31 - 36} \over {2}} \)
\( = {{-5} \over {2}}\)
And \(a_n = -47\)
Using formula \(a_n = a + (n - 1)d\), to find nth term of arithmetic progression,
\(\Rightarrow \) 47 = 18 + (n - 1) \({{-5} \over {2}}\)
\(\Rightarrow \) 36 - \({{5} \over {2}}\) n + \({{5} \over {2}}\)
\(\Rightarrow\) -94 = 36 - 5n + 5
\(\Rightarrow \) 5n = 135
\(\Rightarrow \) n = 27
Therefore, there are 27 terms in the given arithmetic progression.