Consider the arithmetic series 2+9+16+
1. Determine the number of terms in this series
2. Calculate the sum of the series
To determine the number of terms in an arithmetic series, you need to find the common difference (d) first. In this series, you can see that the common difference is 7. Each term is 7 greater than the previous term.
To find the number of terms, you can use the formula for the nth term of an arithmetic series:
An = A1 + (n - 1)d
In this case, A1 = 2 (the first term) and d = 7 (the common difference).
An = 2 + (n - 1)(7)
Since An is not given, we cannot solve for n directly. However, if we continue to list the terms of the series, the next term after 16 would be 23, then 30, and so on.
By observing the pattern, you can see that each term is formed by adding 7 to the previous term. In this case, the last term is 145, and each term increases by 7. So, in this series, there are 21 terms.
To calculate the sum of this series, you can use the formula for the sum of an arithmetic series:
Sn = n/2 * (A1 + An)
In this case, n = 21 (the number of terms), A1 = 2, and An = 145 (the last term).
Sn = 21/2 * (2 + 145)
= 21/2 * 147
= 21 * 73.5
= 1543.5
Therefore, the sum of the series is 1543.5.