find a gp. whose sum upto infinite terms is 3 and the second terms is -18.
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Hi Mate!!!
Sum of infinite terms of g.p is given by
a / ( 1 - r )
Where a is ist term and r is common ratio.
r = Second term / ist term
r = -18 / a
Now put value of r in above formula.
3 = a / 1 - ( -18 / a )
3 = a /{ ( a +18 ) / a }
3 = a² / ( a + 18 )
3a +54 = a²
a² -3a -54 = 0
a = {-3 + 15} / 2 or a = {-3 -15} / 2
a = 6. or. a = -9
........................................................................
Here two g.p series are possible
1). a, ar,ar²,ar³,....arⁿ
a = 6 and r = -3
=>. 6, -18, 54, -162,.....
2) a = -9 and. r = 2
=>. -9, -18, -36,......
Have a nice time...
Sum of infinite terms of g.p is given by
a / ( 1 - r )
Where a is ist term and r is common ratio.
r = Second term / ist term
r = -18 / a
Now put value of r in above formula.
3 = a / 1 - ( -18 / a )
3 = a /{ ( a +18 ) / a }
3 = a² / ( a + 18 )
3a +54 = a²
a² -3a -54 = 0
a = {-3 + 15} / 2 or a = {-3 -15} / 2
a = 6. or. a = -9
........................................................................
Here two g.p series are possible
1). a, ar,ar²,ar³,....arⁿ
a = 6 and r = -3
=>. 6, -18, 54, -162,.....
2) a = -9 and. r = 2
=>. -9, -18, -36,......
Have a nice time...
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