Question 1
128
128
129
129
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Solution: a = 1 4th term = ar^{3} = (8) So r = 2 8th term = ar^{7} = 1 x (2)^{7} = 128
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Question 2
5
3
4
8
Solution: 27, 81,243,…..2187 a = 27 r = \frac{a2}{a1} = \frac{81}{27} = 3 Let n = no. of terms nth term = 2187 = ar^{(n1)} r^{n1} = 81 3^{n1} = 81 n1 = 4 n = 5
Question 3
9
7
r = 2 l= 448 Sum = 889 Let a = first term l = 448 =ar^{n1} =\frac{a\times 2^{n}}{2} a \times 2^{n} = 448 \times 2 = 896 Sum =\frac{ a(r^{n}  1)}{(r1)} = \frac{ a(2^{n}  1)}{(21)} 889 = a\times 2^{n}  a = 896  a a = 896  889 = 7
Question 4
12
19
10
This is a GP with a=2 and r= \frac{1.6}{2} = 0.8 1 < r <1 , So Sum = [latex]\frac{a}{1r}[/latex] = \frac{2}{10.8} = 10
Question 5
4.74 cm
5.44 cm
6 cm
9 cm
Solution: This is a GP with first term, a = 20 r =0.75 and n = 6 Length at nth hours = a x r^{n1} Length at 6th hours = 20 x 0.75^{6  1} = 4.74 cm
Question 6
\frac{5}{9}
\frac{8}{9}
\frac{3}{7}
\frac{10}{9}
Solution: Let a = first term of series. r = \frac{1}{3} Sum = \frac{a}{1r} = 12 a = 12 x (1  r) = 12 x (1  \frac{1}{3} ) = 8 Third term = a\times r^{3  1} = 8 \times (\frac{1}{3})^{2} = \frac{8}{9}
Question 7
+3 or 3
+4 or 3
+5 or 5
+7 or 6
Solution: Let a, ar, ar^{2}, a^{3} be the first four terms of GP a + ar = 16 ar^{2} + ar^{3} = 144 Dividing both, we get \frac{ar^{2} + ar^{3}}{a + ar} = \frac{144}{16} = 9 \frac{ar^{2}(1+r)}{a(1+r)} = 9 r^{2} = 9 So r = +3 or 3
Question 8
18.63
17
15.49
11.65
Solution: GM of AB = \sqrt{ GM of A \times GM of B} = \sqrt{12 \times20} = \sqrt{240} =15.49
Question 9
\frac{11}{12}
\frac{1}{12}
\frac{5}{11}
\frac{10}{19}
Solution: Reciprocal of every term of HP makes up an AP Sum of 7 terms of AP = 84 \frac{7}{2} x ( 2a + 6d) = 84 Solving, a + 3d = 12 Fourth term of AP= a + 3d = 12 Fourth term of HP = \frac{1}{12}
Question 10
\frac{7}{113}
\frac{117}{113}
\frac{11}{13}
\frac{71}{23}
Solution: AP is obtained by taking reciprocal of terms of HP Fourth term of AP = \frac{99}{7} Seventh term of AP = \frac{85}{7} Difference = \frac{9985}{7} = 2 (a + 3d)  (a + 6d) = 2 d = \frac{2}{3} 4th term of AP = a + 3d = \frac{99}{7} a  2 =\frac{99}{7} a = \frac{99}{7} + 2 = \frac{113}{7} So first term of HP = \frac{7}{113}
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