Geometric Progression (G.P.)
1. In each of the following G.P., find
(a) the common ratio (b) the 10th term (c) the th
term
(d) the sum of the first 10 terms (e) the sum of the first terms.
(i) 4, 2, 1, ,, ... (ii) −2, 4, −8, 16, ...
(iii) , − , , − , ... (iv) , , 2, 3, ...
2. The 2nd term of a G.P. is 64 while the 5th term is 27. Find the first 6 terms of the G.P.
3. The fourth term of a G.P. is 9 and the ninth term is 2187. Find the first 4 terms of the G.P.
4. The fourth term of a G.P. is 3 and the sixth term is 147. Find the first 3 terms of the two possible
geometric progressions.
5. The third term of a G.P. of positive terms is and the seventh term is 1 . Find the sum of the
10th and 11th terms of a G.P. giving your answer correct to 2 decimal places?
6. If 3, , , , , 3072 are consecutive terms of a G.P., find the values of , , and .
7. In a G.P., the fifth term exceeds the fourth term by 10 and the fourth term exceeds the third term
by 15. Find the sum of the first 6 terms of the G.P.
8. The product of the first 3 terms of a G.P. is 1 and the product of the third, fourth and fifth terms is
11 . Find the fifth term of a G.P.
9. How many terms of the G.P. , , 2, … must be taken for the sum to exceed one million.
10. The third and sixth terms of a geometric progression are 9 and 2 respectively. Calculate the
common ratio, the first term and the sum to infinity of the progression.
11. The sum of an infinite sequence is 12 and its first term is 3. Find the first four terms of the G.P.
12. In a G.P., the ratio of the sum of first 3 terms to the sum to infinity of the G.P. is 19 : 27. Find the
common ratio.
13. The second term of a G.P. is 2 and its sum to infinity is 9. Find the sum of the first 4 terms of the
two possible geometric progressions.
14. In a G.P. of positive terms, the first term exceeds the third term by 1 and the third term exceeds
the fifth term by . Find the sum to infinity of the G.P.
15. Given that + 18, + 4, − 8 are the first three terms of G.P., find the value of . Hence, find
the common ratio, the fifth term and the sum to infinity.
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1. In each of the following G.P., find
(a) the common ratio (b) the 10th term (c) the th
term
(d) the sum of the first 10 terms (e) the sum of the first terms.
(i) 4, 2, 1, ,, ... (ii) −2, 4, −8, 16, ...
(iii) , − , , − , ... (iv) , , 2, 3, ...
2. The 2nd term of a G.P. is 64 while the 5th term is 27. Find the first 6 terms of the G.P.
3. The fourth term of a G.P. is 9 and the ninth term is 2187. Find the first 4 terms of the G.P.
4. The fourth term of a G.P. is 3 and the sixth term is 147. Find the first 3 terms of the two possible
geometric progressions.
5. The third term of a G.P. of positive terms is and the seventh term is 1 . Find the sum of the
10th and 11th terms of a G.P. giving your answer correct to 2 decimal places?
6. If 3, , , , , 3072 are consecutive terms of a G.P., find the values of , , and .
7. In a G.P., the fifth term exceeds the fourth term by 10 and the fourth term exceeds the third term
by 15. Find the sum of the first 6 terms of the G.P.
8. The product of the first 3 terms of a G.P. is 1 and the product of the third, fourth and fifth terms is
11 . Find the fifth term of a G.P.
9. How many terms of the G.P. , , 2, … must be taken for the sum to exceed one million.
10. The third and sixth terms of a geometric progression are 9 and 2 respectively. Calculate the
common ratio, the first term and the sum to infinity of the progression.
11. The sum of an infinite sequence is 12 and its first term is 3. Find the first four terms of the G.P.
12. In a G.P., the ratio of the sum of first 3 terms to the sum to infinity of the G.P. is 19 : 27. Find the
common ratio.
13. The second term of a G.P. is 2 and its sum to infinity is 9. Find the sum of the first 4 terms of the
two possible geometric progressions.
14. In a G.P. of positive terms, the first term exceeds the third term by 1 and the third term exceeds
the fifth term by . Find the sum to infinity of the G.P.
15. Given that + 18, + 4, − 8 are the first three terms of G.P., find the value of . Hence, find
the common ratio, the fifth term and the sum to infinity.
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