R.S. Aggarwal solutions for Mathematics [English] Class 10 ICSE chapter 11 - Geometric Progression [Latest edition]

Show that the progression 2, 6, 18, 54, 162, ......... is a G.P.

Write its (i) first term (ii) common ratio (iii) nth term (iv) 8th term.

Show that the progression $$625, 125, 25, 5, 1, \frac{1}{5}$$, ......... is a G.P.

Write its (i) first term (ii) common ratio (iii) nth term (iv) 10th term.

Show that the progression $$-27, 9, -3, 1, \frac{-1}{3}$$, ......... is a G.P.

Write its (i) first term (ii) common ratio (iii) nth term (iv) 9th term.

Show that the progression $$2, 2\sqrt{2}, 4, 4\sqrt{2}$$, ......... is a G.P.

Write its (i) first term (ii) common ratio (iii) nth term (iv) 11th term.

Show that the progression $$\frac{-3}{4}, \frac{1}{2}, \frac{-1}{3}, \frac{2}{9}$$ ......... is a G.P.

Write its (i) first term (ii) common ratio (iii) nth term (iv) 6th term.

Show that the progression 0.4, 0.8, 1.6, ......... is a G.P.

Write its (i) first term (ii) common ratio (iii) nth term (iv) 7th term.

Which term of the G.P. 3, 6, 12, 24, ..... is 768?

Which term of the G.P. 5, 10, 20, 40, ..... is 640?

Which term of the G.P. $$\sqrt{3}, 3, 3\sqrt{3}, 9$$, ..... is 729?

Find the G.P. whose 5th and 8th terms are 80 and 640 respectively.

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series

In a Geometric Progression (G.P.), the first term is 24 and the fifth term is 8. Find the ninth term of the G.P.

Find the G.P. whose 4th and 7th terms are $$\frac{1}{18}$$ and $$\frac{-1}{486}$$ respectively.

For what values of $$x$$, the numbers $$(x + 9), (x - 6)$$ and 4 are in G.P.?

Find the 6th term from the end of the G.P. $$16, 8, 4, 2, ......., \frac{1}{512}$$. 

Find the 4th term from the end of the G.P. $$\frac{2}{81}, \frac{2}{27}, \frac{2}{9}, ......., 54$$.

The 4th, 6th and last term of a geometric progression are 10, 40 and 640 respectively. If the common ratio is positive, find the first term, common ratio and the number of terms of the series.

Find the sum of first 8 terms of the G.P. 1, 3, 9, 27, 81, .........

Find the sum of first 10 terms of the G.P. $$1, \sqrt{3}, 3, 3\sqrt{3}, .......$$

Find the sum of first 9 terms of the G.P. $$1, \frac{-1}{2}, \frac{1}{4}, \frac{-1}{8}, .........$$

Find the sum of first 6 terms of the G.P. 0.1, 0.01, 0.001, .........

Find the sum of first 6 terms of the G.P. $$1, \frac{-1}{3}, \frac{1}{3^2}, \frac{-1}{3^3}, ..........$$

The first term of a G.P. is 27 and its 8th term is $$\frac{1}{81}$$. Find the sum of first seven terms of the G.P.

The 4th and the 7th terms of a G.P. are $$\frac{1}{27}$$ and $$\frac{1}{729}$$ respectively. Find the sum of first 6 terms of the G.P.

If the 6th term of a series in Geometric Progression (G.P.) is 32 and the 9th term is 256, find the: 

1. first term and the common ratio.
2. sum of its first 10 terms.

15, 30, 60, 120.... are in G.P. (Geometric Progression):

1. Find the n^th term of this G.P. in terms of n.
2. How many terms of the above G.P. will give the sum 945?

How many terms of the G.P. $$\frac{2}{9}, \frac{-1}{3}, \frac{1}{2}, ............$$ must be taken to make the sum equal to $$\frac{55}{72}$$?

In a G.P. the ratio of the sum of first 3 terms is to that of first 6 terms is 125 : 152. Find the common ratio.

A manufacturer reckons that the value of a machine which costs him ₹31250 depreciates each year by 20%. Find its value after 2 years.

[Hint: Value after 2 years = ₹31250 × $$\left(1 - \frac{20}{100}\right)^2$$.]

Find the sum of the following to n terms: 7 + 77 + 777 + 7777 + ..........

[Hint: $$S_n = 7(1 + 11 + 111 + 1111 +\ .........)$$ $$= \frac{7}{9} (9 + 99 + 999 + 9999 +\ .........)$$
$$= \frac{7}{9} \left[(10 - 1) + (100 - 1) + (1000 - 1)\ .........\right]$$
$$= \frac{7}{9} (10 + 100 + 1000 +\ ....... -1 -1 -1\ ........\ n \text{ times})$$]