A geometric series has a common ratio of (-2) and the first term is 3.
Show that the sum of the first eight positive terms of the series is 65 535.
Answers
Answered by
11
Sequence: Numbers organized in an order.
Series: Sum of the terms of a sequence.
A geometric sequence (here, ) has a common ratio of and the first term is .
If the exponent is even, that term will be positive.
Put in place of ,
Let us define the new sequence that only consists of positive terms. (Here, ) The sequence is defined as,
Finite Geometric Series
The expression reads as "the sum of as goes from to ."
Where,
- is the first term.
- is the common ratio.
- is the term number.
We are given to find the first 8 terms.
The sequence has
- the first term of .
- the common ratio of .
Hence shown.
Similar questions