Write the sum using summation notation, assuming the suggested pattern continues. -9 - 3 + 3 + 9 + ... + 81

Accepted Solution

The sum of the terms of the given sequence will be 648.What is the arithmetic sequence?An arithmetic sequence or arithmetic progression is a sequence in which each term is created or obtained by adding or subtracting a common number to its preceding term or value. The given sequence is representing an arithmetic sequence.Because every successive term of the sequence is having a common difference d = -3 - (-9) = -3 + 9 = 63 - (-3) = 3 + 3 = 6Since last term of the sequence is 81.By the explicit formula of an arithmetic sequence, we can find the number of terms of this sequence.[tex]\rm T_n= a+(n-1)d\\\\[/tex]Where a = first term of the sequence, d = common difference.Substitute all the values in the formula[tex]\rm T_n= a+(n-1)d\\\\ 81 = -9 + 6(n - 1)\\\\ 81+9 =6(n-1)\\\\90=6(n-1)\\\\ n-1=\dfrac{90}{6}\\\\n-1=15\\\\n = 15+1\\\\n=16[/tex]Now we know the sum of an arithmetic sequence is represented by[tex]\rm S_{16}=\dfrac{16}{2}[-9+(16-1)6]\\\\S_{16}=8 [-9+15\times 6]\\\\S_{16}=8 [-9+90}\\\\S_{16} = 8 \times 81\\\\S_{16}=648[/tex]Hence, the sum of the terms of the given sequence will be 648.To know more about arithmetic sequence click the link given below.