1Find the sum of the geometric series \( 2 + 4 + 8 + 16 + \dots \) to 6 terms.
2Find the sum of the geometric series \( \frac{1}{9} + \frac{1}{3} + 1 + \dots \) to 5 terms.
3Find the sum of the geometric series \( -\frac{1}{4} + \frac{1}{2} - 1 + \dots \) to 6 terms.
4Find the sum of the geometric series \( 16 + 8 + 4 + \dots + \frac{1}{16} \).
5Find the sum of the geometric series \( 1 + \frac{1}{3} + \frac{1}{9} + \dots + \frac{1}{729} \).
6A geometric series has first term 2, last term 486, and the sum of all its terms is 728. Find its common ratio.
7A geometric series has first term 5, last term 1215, and the sum of all its terms is 1820. Find its common ratio.
8A geometric series has first term 3, last term 768, and the sum of all its terms is 1533. Find its common ratio.
9The second term of a geometric series is 4 and the seventh term is 128. Find the sum of its first 10 terms.
10The third term of a geometric series is 9 and the fifth term is 81. Find the sum of its first 7 terms.
11How many terms of the geometric series \( 32 + 48 + 72 + \dots \) will have a sum of 665?
12How many terms of the geometric series \( 6 - 12 + 24 - 48 + \dots \) will have a sum of \( -2046 \)?
13Sarita borrowed Rs. 43,680 from her friend Garima and agreed to pay it back in 6 instalments. If each instalment was three times the previous one, find the difference between the first and the last instalments.
14Why is the series multiplied by \( r \) when the sum formula is derived?
15Why can the sum formula not be used when \( r = 1 \)? What is the sum then?
16The sum of the first 6 terms of a geometric series with common ratio 2 is 189. Find the first term.
17Sita saves Rs. 5 on the first day, and every day after that she saves twice what she saved the day before. How much has she saved in 10 days?