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For the arithmetic sequence beginning with the terms {9,14, 19,24,29,34dots }, what is the sum of the first 23 terms?

User Mythbu
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2 Answers

5 votes

Answer:

S23 = 1472

Step-by-step explanation:

our 23rd term will be 9+ 22*5 = 1+110 = 119

Sum will be equal to 23(9+119)/2 = 23*128/2 = 23*64 = 1472

User Htechno
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4 votes

Final answer:

The sum of the first 23 terms of the arithmetic sequence {9,14,19,24,29,34,...} is 1472. This is calculated using the sum formula for arithmetic series and the common difference of the sequence.

Step-by-step explanation:

To calculate the sum of the first 23 terms of the given arithmetic sequence {9,14,19,24,29,34,...}, we'll use the formula for the sum of an arithmetic series, which is Sn = (n/2)(a1 + an). In this formula, n is the number of terms, a1 is the first term, and an is the last term.

First, we need to find the 23rd term using the formula an = a1 + (n-1)d, where d is the common difference. In this sequence, the common difference is 5, since each term is 5 more than the previous one. So, the 23rd term is a23 = 9 + (23-1)*5 = 9 + 110 = 119.

Now we can plug these values into the sum formula: S23 = (23/2)(9 + 119) = (23/2)*128 = 23*64 = 1472. Thus, the sum of the first 23 terms is 1472.

User Justin Lange
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