1.1what happens to the following arithemetic series if it continues indefinitely? 2+5+8+11+14+17+20+.....so S§=?
Nothing very exciting.
It just blows up, getting bigger and bigger
You are just adding 3 to each new term added.
Owk Reinny if I come across diz kind of Question in exam I shuld just write that it will increase by three till infinity
Of course not.
It only increases by 3 for this question since this arithmetic series has a common difference of 3
It depends totally on the sequence
To find the sum of an arithmetic series, you need to know the first term (a), the common difference (d), and the number of terms (n). Let's first determine the common difference, d.
In the given series 2+5+8+11+14+17+20+..., the first term (a) is 2, and the common difference (d) can be obtained by subtracting any two consecutive terms. By subtracting 2 from 5 or 5 from 8, we can see that the common difference is 3.
Now that we have the common difference, we can find the sum of the series. However, since the series continues indefinitely, we need to find the sum of an infinite geometric series. The formula for the sum of an infinite geometric series is:
S = a / (1 - r), where S represents the sum, a is the first term, and r is the common ratio.
In our case, the common ratio (r) can be determined by dividing the common difference (d) by the first term (a). Therefore, r = d / a = 3 / 2 = 1.5.
Plugging in the values into the formula, we have:
S = 2 / (1 - 1.5).
However, to solve this formula, we need the common ratio to be between -1 and 1. Since our common ratio (1.5) does not fall within this range, the sum of the infinite series is not defined.
Therefore, the answer to S is undefined as the series does not have a sum.