In a sequence of (4n + 1) terms the first (2n + 1) terms are in AP whose common difference is 2, and the last (2n + 1) terms are in GP whose common ratio 0.5. If the middle terms of the AP and GP are equal, then
(i) Middle term of the sequence is
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)a (ii)b
Sol--
Let 1 st term be a . and common difference is 2 ; T 2n + 1 = a + 4n = A (say) r = 
Middle term of AP = T n + 1 ; Middle term of GP = T 3n + 1
T n + 1 = a + 2n ⇒ T 3n + 1 = A . r n = 
(a + 2n) = 
⇒ 2 n a + 2n2 n = a + 4n
a = 
⇒ T 2n + 1 = a + 4n = 
+ 4n = 
= 
T 3n + 1 = 
= 
= 
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