if if SN = 3 n -1 find a3
Answers
Step-by-step explanation:
Finding the Sum of a Series Given our generic arithmetic sequence a1, a2, a3, a4, ..., we can add the terms, called a series, as follows: a1 + a2 + a3 + a4 + ... + an. Given the formula for the general term an = dn + c, there exists a formula that can add such a finite list of these numbers. It requires three pieces of information. The formula is... Sn = ½n(a1 + an) ...where Sn is the sum of the first n numbers, a1 is the first number in the sequence and an is the last number in the sequence.
Usually problems present themselves in either of two ways. Either the first number in the sequence and the number of terms are known or the first number and the last number of the sequence are known.
Let's take a finite portion of sequence B and experience our first case. If we had 26, 31, 36, 41, 46, ... and knew that there were 50 terms in the sequence, then we have a1 = 26 and n = 50. We would have to develop a formula for the nth term so we could calculate a50, the last term in the sequence. Since we already calculated the formula above, sdoklfjsdokfjoidsj3veo'sjmd3ove4jdsfomsdlkcjsoeifdsnvk;sdnfvousdefwdjsvmosedjfromvoidrsf0jsdvcmdso4fjvsdmvl58dsjfdvnsdvlkdswe can use it to calculate a50. It is an = 5n + 21 is the formula so a50 = 5(50) + 21 = 250 + 21 = 271. Now we can plug the numbers into the formula and gain a solution. S50 = ½(50)(26 + 271) = 25(297) = 7425. This means that the sum of the first 50 terms is 7425.
Next, let's take a portion of sequence A for our second possible situation. If we were dealing with 5, 8, 11, 14, 17, ... , 128, then we would know that a1 = 5 and an = 128. If we knew the number of terms in this sequence, we would be able to use the formula. Finding n becomes our next task. Since we know the formula for the general term, an = 3n + 2, we can use it to find the number of terms in this sequence. We set the last term equal to the formula and solve for n. We get 128 = 3n + 2, which means that n = 42 and a42 = 128. Now we can plug the information into the sum formula and get S42 = ½(42)(5 + 128) = (21)(133) = 2793, which must be the sum of the first 42 terms in the sequence.