find the g.p whose 4th term is 1/18 and 7th term -1/486
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Given that the 4th term = 1/18.
Therefore t4 = 1/18 = > ar^3 = 1/18 --------------- (1).
Given that the 7th term = -1/486.
Therefore t7 = -1/486 = > ar^6 = -1/486 ----------- (2)
On solving (2) & (1) we get
ar^6/ar^3 = -1/486/1/18
r^6 - 3 = -18/486
r^3 = -1/27
r = -1/3.
Substitute r = -1/3 in (2), we get
ar^6 = -1/486
a(-1/3)^6 = -1/486
1/729 a = -1/486
Multiply both sides by 729
729 * (1/729 * a) = 729 * (-1/486)
a = -729/486
a = -3/2.
Therefore the first term of the GP is -3/2 and the common ratio is -1/3.
Therefore the General form of the GP = -3/2,1/2, -1/6,1/18....
Hope this helps!
Therefore t4 = 1/18 = > ar^3 = 1/18 --------------- (1).
Given that the 7th term = -1/486.
Therefore t7 = -1/486 = > ar^6 = -1/486 ----------- (2)
On solving (2) & (1) we get
ar^6/ar^3 = -1/486/1/18
r^6 - 3 = -18/486
r^3 = -1/27
r = -1/3.
Substitute r = -1/3 in (2), we get
ar^6 = -1/486
a(-1/3)^6 = -1/486
1/729 a = -1/486
Multiply both sides by 729
729 * (1/729 * a) = 729 * (-1/486)
a = -729/486
a = -3/2.
Therefore the first term of the GP is -3/2 and the common ratio is -1/3.
Therefore the General form of the GP = -3/2,1/2, -1/6,1/18....
Hope this helps!
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