# 11.5.4. Arithmetic Series

Determine .

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Determine the number of terms of the arithmetic sequence whose first and last terms are 11 and 81 respectively, given that the sum of all its terms is 506.

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Starting from the first term of the arithmetic sequence , find the number of terms whose sum equals .

• A
• B
• C
• D
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Find the sum of the first 17 terms of the arithmetic series .

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Find the sum of terms in the arithmetic sequence starting from up to .

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A body fell freely from a height of meters under the effect of gravity. It covered distances of , , and meters in the first three seconds respectively. Neglecting the air resistance, determine the total distance covered after 13 seconds.

• Ameters
• Bmeters
• Cmeters
• Dmeters
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Find the arithmetic sequence whose , , and .

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• D
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A runner is preparing himself for a long-distance race. He covered km on the first day, then increased the distance by 0.5 kilometers daily. Find the sum of the distances that the runner covered in the first 14 days.

• Akm
• Bkm
• Ckm
• Dkm
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A runner is practicing for a long distance race, where the plan is to run km on the first day and to do 0.7 kilometers more every day. In how many days will the runner cover the distance of km provided that the plan is followed properly?

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Find the sum of the natural numbers that are greater than 29, less than 97, and divisible by 3.

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Determine the sum of the terms in the arithmetic sequence starting from its first term.

• A
• B
• C
• D
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If the sum of terms of an arithmetic sequence is identified by , find .

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Find the sum of the first 31 terms of the sequence .

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The sum of -terms of an arithmetic sequence is identified by the rule . Find the number of terms, starting from the first term, whose sum is 468.

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Starting from the first term of the sequence , determine the number of terms that null the sum.

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Starting from the first term of the sequence , determine the least number of terms that result in a negative sum.

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