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Find an expression for the general term and calculate the term as indicated in the sequence of this A.P : 1/2 , 3/4 , . , . , 6th term, 9th term, 14th term.
SOLUTION
General term formula = Gn = a + ( n - 1 ) *d
a = 1/2
C. d = common difference
= 2th term _ 1st term
= 3/4 _ 1/2
= 1/4 .
Gn = 1/2 + ( n _ 1 )* 1/4
= 1/2 + ( n/4 _ 1/4 )
= 1/2 + ( n _ 1 / 4 )
= 1/2 + n_ 1/4
= 1 + n/4 .
_________
(i) 6th term = 1+ n /4
= 1+ 6/4 = 7/4 .ans.
(ii) 9th term = 1+n/4
= 1+9/4 = 10/4 or 5/2 .ans.
(iii) 14th term = 1+n/4
= 1+14/4 = 15/4 .ans.
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