T2= 2√2 ,T9=32 then find the common ratio (it is GP).
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Let the first term of G.P be 'a'
Let the common difference be 'r'
nth term of G.P = ar^(n-1)
t2 = ar^(2-1)
t2 = ar = 2√2
nth term of G.P = ar^(n-1)
t9 = ar^(9-1)
t9 = ar^8 = 32
t9/t2 = r^7 = 32/2√2 = 16/√2
=> r^7 = 16/√2
=> r^7 = √256/√2
=> r^7 = √(256/2)
=> r^7 = √128
=> r^14 = 128
=> r^14 = 2^7
=> r = √2
The common difference of G.P is √2
Let the common difference be 'r'
nth term of G.P = ar^(n-1)
t2 = ar^(2-1)
t2 = ar = 2√2
nth term of G.P = ar^(n-1)
t9 = ar^(9-1)
t9 = ar^8 = 32
t9/t2 = r^7 = 32/2√2 = 16/√2
=> r^7 = 16/√2
=> r^7 = √256/√2
=> r^7 = √(256/2)
=> r^7 = √128
=> r^14 = 128
=> r^14 = 2^7
=> r = √2
The common difference of G.P is √2
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