Question -
Answer -
(i) the ninth term of theG.P. 1, 4, 16, 64, ….
We know that,
t1 = a= 1, r = t2/t1 = 4/1 = 4
By using the formula,
Tn =arn-1
T9 = 1(4)9-1
= 1 (4)8
= 48
(ii) the 10th termof the G.P. -3/4, ½, -1/3, 2/9, ….
We know that,
t1 = a= -3/4, r = t2/t1 = (1/2) / (-3/4) = ½ × -4/3 = -2/3
By using the formula,
Tn =arn-1
T10 =-3/4 (-2/3)10-1
= -3/4 (-2/3)9
= ½ (2/3)8
(iii) the 8th termof the G.P., 0.3, 0.06, 0.012, ….
We know that,
t1 = a= 0.3, r = t2/t1 = 0.06/0.3 = 0.2
By using the formula,
Tn =arn-1
T8 =0.3 (0.2)8-1
= 0.3 (0.2)7
(iv) the 12th termof the G.P. 1/a3x3 , ax, a5x5,….
We know that,
t1 = a= 1/a3x3, r = t2/t1 = ax/(1/a3x3)= ax (a3x3) = a4x4
By using the formula,
Tn =arn-1
T12 =1/a3x3 (a4x4)12-1
= 1/a3x3 (a4x4)11
= (ax)41
(v) nth term of the G.P.√3, 1/√3, 1/3√3, …
We know that,
t1 = a= √3, r = t2/t1 = (1/√3)/√3 = 1/(√3×√3) = 1/3
By using the formula,
Tn =arn-1
Tn =√3 (1/3)n-1
(vi) the 10th termof the G.P. √2, 1/√2, 1/2√2, ….
We know that,
t1 = a= √2, r = t2/t1 = (1/√2)/√2 = 1/(√2×√2) = 1/2
By using the formula,
Tn =arn-1
T10 =√2 (1/2)10-1
= √2 (1/2)9
= 1/√2 (1/2)8