Find the total number of terms in the given arithmetic sequence.a1=−296,d=−13,S=−36

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Aubree Mcintyre · Accepted Answer

Step 1 The first term of the arithmetic sequence is given as −296 The common difference of the arithmetic sequence is 13 The sum of the terms is given as -36 Step 2 If the number of terms is n, then the sum of the arithmetic sequence is given as Sn=n2[2a1+(n−1)d] −36=n2[2⋅(−296)+(n−1)⋅13] −72=n[−296+(n−1)13] −72=−29n3+n(n−1)13 −72=−29n+n(n−1)3 −72=−29n+n2−n3 −216=−30n+n2 n2−30n+216=0 Using the quadratic equation formula, we get n=−(−30)±(−30)2−4(1)(216)2⋅1 =30±900−8642 =30±362 =30±62 =30−62 and 30+62 =242 and 362 =12 and 18 Therefore, the number of terms is either 12 or 18.

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Eliza Beth13 · Accepted Answer

To find the total number of terms in the given arithmetic sequence, we&#039;ll use the formula:S=n2(2a1+(n−1)d)Given:a1=−296,d=−13,S=−36Substituting the given values into the formula, we get:−36=n2(2(−296)+(n−1)(−13))Simplifying further:−36=n2(−586−n−13)−36=n2(−586−n−13)−36=n2(−586−n−13)Multiplying through by 6 to clear the fractions:−216=n(−581−2(n−1))−216=n(−58−2n+2)−216=n(−2n−56)−216=−2n2−56nRearranging the equation:2n2+56n−216=0Now, we can solve this quadratic equation using the quadratic formula:n=−b±b2−4ac2aSubstituting the values into the formula, we get:n=−56±562−4(2)(−216)2(2)Simplifying:n=−56±3136+17284n=−56±48644n=−56±16194n=−14±4191Thus, the total number of terms in the given arithmetic sequence is −14±419.

Mr Solver · Accepted Answer

Given: a1=−296, d=−13, and S=−36.We can substitute the given values into the formula and solve for n:−36=n2(2(−296)+(n−1)(−13))Simplifying the equation:−36=n2(−586−n−13)Multiplying both sides by 2 to eliminate the fraction:−72=n(−586−n−13)Expanding and rearranging:−72=n(−586−n3+13)Simplifying further:−72=n(−586−n3+13)To solve this quadratic equation, we can multiply both sides by 6 to eliminate the fraction:−432=n(−58−2n+2)Expanding and rearranging:−432=n(−2n−56)Simplifying further:−432=−2n2−56nRearranging the equation to bring it to standard quadratic form:2n2+56n−432=0Now, we can solve this quadratic equation using any suitable method (factoring, completing the square, quadratic formula, etc.) to find the values of n.

madeleinejames20 · Accepted Answer

Solution:S=n2(2a1+(n−1)d)where:- S represents the sum of the series- n represents the number of terms- a1 represents the first term of the series- d represents the common difference between termsGiven:a1=−296d=−13S=−36Substituting the given values into the formula, we have:−36=n2(2(−296)+(n−1)(−13))To simplify the equation, we can multiply through by 2 to eliminate the fraction:−72=n(−293+(n−1)(−13))Next, we can distribute the terms inside the parentheses:−72=n(−293−n−13)Now, we can simplify further:−72=n(−29−n+13)Combining like terms:−72=n(−n−283)To eliminate the fraction, we can multiply both sides by 3:−216=n(−n−28)Expanding the equation:−216=−n2−28nRearranging the equation to bring all terms to one side:n2+28n−216=0To solve this quadratic equation, we can factorize it or use the quadratic formula. Factoring, we have:(n+18)(n−12)=0Setting each factor equal to zero:n+18=0orn−12=0Solving for n:n=−18orn=12Since the number of terms cannot be negative, we discard the solution n=−18. Therefore, the total number of terms in the given arithmetic sequence is n=12.

Find the number of terms in the arithmetic sequence with

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