## Geometric Sequences Problems with Answers

Q1. Find the 10th term of a geometric sequence if a_{1} = 45 and the common ratio r = 0.2.

Ans: 2.304×10^{−5}

Q2. ‘x’ and ‘y’ are two numbers whose AM is 25 and GM is 7. Find the numbers.

Ans: x = 1 and y = 49.

Q3. Determine the common ratio r of a geometric progression with the first term is 5 and the fourth term is 40.

Ans: 2

Q4. The sum of the first three terms of a G.P. is 21/2 and their product is 27. Find the common ratio.

Ans: 2 and ½

Q5. If the 4th,10th and 16th terms of a GP are x, y, and z respectively, then prove that x,y, and z are in GP.

see also: Class 11 Maths

Q6. If the first term and the nth term of a GP are a and b respectively, and if P is the product of n terms then prove that P^{2}=(ab)^{n}

Q7. Find three numbers in G.P. whose sum is 65 and whose product is 3375.

Ans: *5, 15, 45.*

Q8. Find the sum of 2, 6, 18, … to 7 terms.

Ans: 2186

Q9. Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

Ans: 9 and 27

**Q10. Find the sum of the following series :**

**(i) 5 + 55 + 555 + … to n terms.**

Ans:

**(ii) 7 + 77 + 777 + … to n terms.**

Ans: *7/81 (10 ^{n+1} – 9n – 10)*

**(iii) 9 + 99 + 999 + … to n terms.**

Ans: * 1/9 [10 ^{n+1} – 9n – 10]*

**(iv) 0.5 + 0.55 + 0.555 + …. to n terms**

Ans: *5/9 [n – 1/9 (1 – 1/10 ^{n})]*

**(v) 0.6 + 0.66 + 0.666 + …. to n terms.**

Ans: *6/9 [n – 1/9 (1 – 1/10 ^{n})]*

Q11. The non-zero numbers a,b and c are in AP if we increase a by 2, the numbers become in G.P. Find the value of b−a.

Ans: **√**{2(2b−a)}

Q12. How many terms of the series 2 + 6 + 18 + …. Must be taken to make the sum equal to 728?

Ans: 6

Q13. Find t if 3,12,t are in GP

Ans: 48

Very beautifully explained everything in these handwritten notes …..Good for revision before neet /boards exams👌🏻