Question

Write the sum using summation notation, assuming the suggested pattern continues.

Answer 1

Answer:

Sum of the sequence will be 648

Step-by-step explanation:

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 = 6

3 - (-3) = 3 + 3 = 6

Since last term of the sequence is 81

Therefore, by the explicit formula of an arithmetic sequence we can find the number of terms of this sequence

$T_{n}=a+(n-1)d$

where a = first term of the sequence

d = common difference

n = number of terms

81 = -9 + 6(n - 1)

81 + 9 = 6(n - 1)

n - 1 = $\frac{90}{6}=15$

n = 15 + 1 = 16

Now we know sum of an arithmetic sequence is represented by

$\sum_{n=1}^{n}(a_{n})=\frac{n}{2}(a_{1}+a_{n})$

Now we have to find the sum of the given sequence

$S_{16}=\frac{16}{2}[-9 + (16-1)6]$

              = 8[-9 + 90]

              = 8×81

              = 648

Therefore, sum of the terms of the given sequence will be 648.