ICSE Class 10 Geometric Progression — Mock Test (2027)

Free online mock test for Geometric Progression (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.

Sample questions

1. 1.What is the sum $n$ terms of GP 5, $\frac{20}{7}, \frac{80}{49}, \ldots$
   • A.$\frac{3}{35} \left[1 - \left(\frac{4}{7}\right)^n\right]$
   • B.$\frac{3}{35} \left[1 - \left(\frac{4}{7}\right)^{40}\right]$
   • C.$\frac{35}{3} \left[1 - \left(\frac{4}{7}\right)^n\right]$
   • D.$\frac{35}{3} \left[1 - \left(\frac{4}{7}\right)^{n-1}\right]$
2. 2.In a geometric progression, the $4^{th}$ term is 54, the $7^{th}$ term is 1458, and the last term is 13122. What are the common ratio, first term, number of terms, and their sum?
   • A.Common ratio = 2, First term = 3, Number of terms = 8, Sum = 765
   • B.Common ratio = 3, First term = 2, Number of terms = 9, Sum = 19682
   • C.Common ratio = 4, First term = 1, Number of terms = 7, Sum = 5461
   • D.Common ratio = 3, First term = 6, Number of terms = 8, Sum = 19680
3. 3.Find the fifth term from the end of the series 243, 81, 27, 9, ..., $ \frac{1}{729} $.
4. 4.Find the sum of the geometric progression 0.15, 0.015, 0.0015, ... up to 30 terms.
   • A.$S_{30} = \frac{3}{17} \left(1 - \frac{1}{10^{30}}\right)$
   • B.$S_{30} = \frac{1}{6} \left(1 - \frac{1}{10^{30}}\right)$
   • C.$S_{30} = \frac{3}{20} \left(1 - \frac{1}{10^{30}}\right)$
   • D.$S_{30} = \frac{15}{17} \left(1 - \frac{1}{10^{30}}\right)$
5. 5.If $a, b$ and $c$ are in G.P., which of the following proves that $\frac{1}{a + b}, \frac{1}{2b}$ and $\frac{1}{b + c}$ are in A.P.?
   • A.$\frac{1}{a + b} + \frac{1}{b + c} = \frac{1}{b}$
   • B.$\frac{1}{a + b} + \frac{1}{b + c} = \frac{2}{b}$
   • C.$\frac{1}{a + b} \times \frac{1}{b + c} = \frac{1}{b^2}$
   • D.$\frac{1}{a + b} - \frac{1}{b + c} = \frac{1}{b}$