Final answer:
To find the number of terms in the arithmetic sequence that will give a sum of 2332, we use the formula for the sum of an arithmetic sequence. By trial and error, we find that 17 terms of the given sequence will give a sum of 2332.
Step-by-step explanation:
To find the number of terms in the arithmetic sequence that will give a sum of 2332, we need to first determine the common difference, which is the difference between consecutive terms. In this sequence, the common difference is 22 - 1 = 21.
The formula to find the sum of an arithmetic sequence is:
S = (n/2)(2a + (n-1)d)
where S is the sum, a is the first term, d is the common difference, and n is the number of terms.
Given that the sum is 2332 and the first term is 1, we can solve for n as follows:
2332 = (n/2)(2(1) + (n-1)(21))
Simplifying:
2332 = (n/2)(2 + 21n - 21)
2332 = (n/2)(21n - 19)
Dividing both sides by 21:
111 = (n/2)(n - 19)
Since n is a positive integer, we can try different values of n to find the solution. By trial and error, we find that n = 17 satisfies the equation.
Therefore, 17 terms of the arithmetic sequence {1, 22, 43, 64, 85, ...} will give a sum of 2332.