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Answers
The n th term is given by the formula 9 n + 5 .
a )
Let n = 1 .
Let a be the first term .
a = 9(1) + 5
⇒ a = 9 + 5
⇒ a = 14
Let d be the common difference .
a + d = 9(2) + 5
⇒ a + d = 18 + 5
⇒ a + d = 23
a + d - a = 23 - 14
⇒ d = 9
a = 14
d = 9
OPTION VERIFICATION :
(i) 14 is clearly in the sequence .
(ii) Let 99 be the n th term .
n th term = a + ( n - 1 ) d
99 = 14 + 9( n - 1 )
⇒ 9 ( n - 1 ) = 85
⇒ n - 1 = 85/9
Hence n is not an integer .
99 is not in sequence .
(iii) 860
860 = 14 + 9( n - 1 )
⇒ 846 = 9( n - 1 )
⇒ n - 1 = 846/9
⇒ n - 1 = 94
⇒ n = 95
n is an integer and hence it is a term .
(iv) a starts from 14 .
Hence every term has to be greater than 14 .
Since -4 < 14 , it is not a term .
b )
The n th term is 9 n - 5
So :
9 n + 5 = 383
⇒ 9 n = 383 - 5
⇒ 9 n = 378
⇒ n = 378/9
⇒ n = 42
383 is the 42nd term .
c )
Let n th term be greater than 1000 .
a + ( n - 1 )d > 1000
⇒ 14 + 9 n - 9 > 1000
⇒ 9 n + 5 > 1000
⇒ 9 n > 995
⇒ n > 995/9
⇒ n ≈ 110.55
So n = 111 th term .
111 th term is more than 1000 .
Answer:
a + ( n - 1 )d > 1000
14 + 9 n - 9 > 1000
9 n + 5 > 1000
9 n > 995
n > 995/9
n ≈ 110.55
So n = 111 th term .
Step-by-step explanation: