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# Sequences: Consecutive Integers - Calculating the Sum of Consecutive Integers

What is the sum of the terms in a certain sequence of consecutive integers? >(1) The least term in the sequence is 8. >(2) The average (arithmetic mean) of terms is 16.
Incorrect. [[snippet]] Stat. (1): The value of the least number of the set does not tell you how many terms are there, nor their average. Stat.(1) → IS → BCE.
Incorrect. [[snippet]] Stat. (2): The average of the terms in the set is a useful piece of information, but you're still missing the number of terms in the set. If the set includes 3 terms or 30 terms, the sum of the set will be completely different. Stat.(2) → IS → ACE.
Correct. [[snippet]] Stat. (1): The value of the least number of the set does not tell you how many terms are there, nor their average. Stat.(1) → IS → BCE. Stat. (2): The average of the terms in the set is a useful piece of information, but you're still missing the number of terms in the set. If the set includes 3 terms or 30 terms, the sum of the set will be completely different. Stat.(2) → IS → CE. Stat. (1)+(2): Recall that the average of a set of consecutive integers is also the average of the first and last terms. So if the least term is 8 and the greatest term is $$x$$, then >$$\frac{8 + x}{2} = 16$$, according to Stat. (2). From here it is possible to find the largest term $$x$$, and the number of terms can also be found – simply count the number of consecutive integers between 8 and $$x$$. You have what you need to find the sum of the terms in the set, so Stat.(1+2) → S → C.
Incorrect. [[snippet]] Stat. (1)+(2): Recall that the average of a set of consecutive integers is also the average of the first and last terms. So if the least term is 8 and the greatest term is $$x$$, then >$$\frac{8 + x}{2} = 16$$, according to Stat. (2). From here it is possible to find the largest term $$x$$, and the number of terms can also be found – simply count the number of consecutive integers between 8 and $$x$$. You have what you need to find the sum of the terms in the set, so Stat.(1+2) → S → C.
Incorrect. [[snippet]] Stat. (1): The value of the least number of the set does not tell you how many terms are there, nor their average. Stat.(1) → IS → BCE. Stat. (2): The average of the terms in the set is a useful piece of information, but you're still missing the number of terms in the set. If the set includes 3 terms or 30 terms, the sum of the set will be completely different. Stat.(2) → IS → CE.
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.