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If the second term and fifth term of the geometric series are 15 and 405 respectively, find the sum of first 6 terms of the series
1) Define sequence and series.

→ Sequence: A set of numbers which is formed under a definite mathematical rule is called a sequence. 1, 3, 5, and, 2, 4, 8, ..., are the example of sequence.

Series: The sum of the terms of a sequence is called a series. The sum of the terms of the series is denoted by Sn. 1+3+5+... + n, 2+4+8+ + n are the example of series.

2) Define arithmetic sequence. ⇒ A sequence having same difference between the successive terms is called arithmetic sequence.

3) Define geometric sequence. The sequence in which the ratio of any term to the preceding term is constant is called geometric sequence. The constant is called common ratio. ←

4) Define arithmetic mean.

⇒ In arithmetic sequence the term between the first term and last term is called arithmetic mean.

5) Define geometric mean.

← In geometric sequence the term between the first and last term is called geometric mean.