Advertisements
Advertisements
प्रश्न
If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
पर्याय
(a) 1/4
(b) 1/2
(c) 2
(d) 4
उत्तर
(d) 4
\[a_2 = 2 \]
\[ \therefore ar = 2 . . . . . . . . (i)\]
\[\text{ Also }, S_\infty = 8\]
\[ \Rightarrow \frac{a}{\left( 1 - r \right)} = 8\]
\[ \Rightarrow \frac{a}{\left( 1 - \frac{2}{a} \right)} = 8 \left[ \text{ Using } (i) \right]\]
\[ \Rightarrow a^2 = 8\left( a - 2 \right)\]
\[ \Rightarrow a^2 - 8a + 16 = 0\]
\[ \Rightarrow \left( a - 4 \right)^2 = 0\]
\[ \Rightarrow a = 4\]
\[\]
APPEARS IN
संबंधित प्रश्न
Which term of the following sequence:
`sqrt3, 3, 3sqrt3`, .... is 729?
Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015,…
Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.
Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
Which term of the G.P. :
\[\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, \frac{1}{4\sqrt{2}}, . . . \text { is }\frac{1}{512\sqrt{2}}?\]
Find the 4th term from the end of the G.P.
\[\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, . . . , \frac{1}{4374}\]
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
Find three numbers in G.P. whose sum is 38 and their product is 1728.
The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.
Find the sum of the following series:
0.5 + 0.55 + 0.555 + ... to n terms.
The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.
How many terms of the G.P. 3, \[\frac{3}{2}, \frac{3}{4}\] ..... are needed to give the sum \[\frac{3069}{512}\] ?
Prove that: (91/3 . 91/9 . 91/27 ... ∞) = 3.
Prove that: (21/4 . 41/8 . 81/16. 161/32 ... ∞) = 2.
If Sp denotes the sum of the series 1 + rp + r2p + ... to ∞ and sp the sum of the series 1 − rp + r2p − ... to ∞, prove that Sp + sp = 2 . S2p.
Find the rational number whose decimal expansion is \[0 . 423\].
The sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.
If a, b, c are in G.P., then prove that:
If a, b, c are in A.P., b,c,d are in G.P. and \[\frac{1}{c}, \frac{1}{d}, \frac{1}{e}\] are in A.P., prove that a, c,e are in G.P.
If pth, qth and rth terms of an A.P. and G.P. are both a, b and c respectively, show that \[a^{b - c} b^{c - a} c^{a - b} = 1\]
Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .
Find the geometric means of the following pairs of number:
2 and 8
Find the geometric means of the following pairs of number:
a3b and ab3
If the fifth term of a G.P. is 2, then write the product of its 9 terms.
If the first term of a G.P. a1, a2, a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is
If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is
Check whether the following sequence is G.P. If so, write tn.
2, 6, 18, 54, …
For the G.P. if a = `2/3`, t6 = 162, find r.
For the following G.P.s, find Sn
0.7, 0.07, 0.007, .....
For a G.P. if S5 = 1023 , r = 4, Find a
For a G.P. if a = 2, r = 3, Sn = 242 find n
For a G.P. If t4 = 16, t9 = 512, find S10
If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.
Select the correct answer from the given alternative.
The common ratio for the G.P. 0.12, 0.24, 0.48, is –
Select the correct answer from the given alternative.
If common ratio of the G.P is 5, 5th term is 1875, the first term is -
Answer the following:
If p, q, r, s are in G.P., show that (pn + qn), (qn + rn) , (rn + sn) are also in G.P.
If 0 < x, y, a, b < 1, then the sum of the infinite terms of the series `sqrt(x)(sqrt(a) + sqrt(x)) + sqrt(x)(sqrt(ab) + sqrt(xy)) + sqrt(x)(bsqrt(a) + ysqrt(x)) + ...` is ______.
