pc2-brazil said:[itex]2a=27-27r[/itex] (1)
[itex]a-ar^3=13-13r[/itex] (2)
Put 27 in evidence in (1) and put 13 in evidence in (2).
[itex]2a=27(1-r)[/itex] (1)
[itex]a-ar^3=13(1-r)[/itex] (2)
Now divide (2) by (1).
pc2-brazil said:[itex]2a=27-27r[/itex] (1)
[itex]a-ar^3=13-13r[/itex] (2)
Put 27 in evidence in (1) and put 13 in evidence in (2).
[itex]2a=27(1-r)[/itex] (1)
[itex]a-ar^3=13(1-r)[/itex] (2)
Now divide (2) by (1).
That is correct. I suppose you also found that r = 1/3.thornluke said:I found that a =9.
An infinite geometric sequence is a series of numbers where each term is found by multiplying the previous term by a constant value. The sequence continues infinitely, creating a pattern of numbers that either increase or decrease in a predictable way.
The first term, also known as the initial term, is the first number in the sequence. It is denoted by 'a' and is typically given in the problem or can be calculated using the formula a1 = a0 * r, where a0 is the first term and r is the common ratio.
To find the common ratio, you can divide any term in the sequence by the previous term. The resulting quotient will be the common ratio. Alternatively, you can use the formula r = an/an-1, where an and an-1 are two consecutive terms in the sequence.
The formula for finding the nth term of an infinite geometric sequence is an = a1 * rn-1, where a1 is the first term, r is the common ratio, and n is the term number. This formula applies as long as the sequence is infinite and follows the geometric pattern.
The sum of the first n terms of an infinite geometric sequence can be found using the formula Sn = a1 * (1 - rn)/(1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms. This formula only applies when the common ratio is between -1 and 1, otherwise the sum will not converge to a finite value.