Answer:
-1,512,390
Step-by-step explanation:
Given
a1 = 15
![a_i = a_{i-1} -7](https://tex.z-dn.net/?f=a_i%20%3D%20a_%7Bi-1%7D%20-7)
Let us generate the first three terms of the sequence
![a_2 = a_{2-1}-7\\a_2 = a_1 - 7\\a_2 = 15-7\\a_2 = 8](https://tex.z-dn.net/?f=a_2%20%3D%20a_%7B2-1%7D-7%5C%5Ca_2%20%3D%20a_1%20-%207%5C%5Ca_2%20%3D%2015-7%5C%5Ca_2%20%3D%208)
For ![a_3](https://tex.z-dn.net/?f=a_3)
![a_3 = a_{3-1}-7\\a_3 = a_2 - 7\\a_3 = 8-7\\a_3 = 1](https://tex.z-dn.net/?f=a_3%20%3D%20a_%7B3-1%7D-7%5C%5Ca_3%20%3D%20a_2%20-%207%5C%5Ca_3%20%3D%208-7%5C%5Ca_3%20%3D%201)
Hence the first three terms ae 15, 8, 1...
This sequence forms an arithmetic progression with;
first term a = 15
common difference d = 8 - 15 = - -8 = -7
n is the number of terms = 660 (since we are looking for the sum of the first 660 terms)
Using the formula;
![S_n = \frac{n}{2}[2a + (n-1)d]\\](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B2a%20%2B%20%28n-1%29d%5D%5C%5C)
Substitute the given values;
![S_{660} = \frac{660}{2}[2(15) + (660-1)(-7)]\\S_{660} = 330[30 + (659)(-7)]\\S_{660} = 330[30 -4613]\\S_{660} = 330[-4583]\\S_{660} = -1,512,390](https://tex.z-dn.net/?f=S_%7B660%7D%20%3D%20%5Cfrac%7B660%7D%7B2%7D%5B2%2815%29%20%2B%20%28660-1%29%28-7%29%5D%5C%5CS_%7B660%7D%20%3D%20330%5B30%20%2B%20%28659%29%28-7%29%5D%5C%5CS_%7B660%7D%20%3D%20330%5B30%20-4613%5D%5C%5CS_%7B660%7D%20%3D%20330%5B-4583%5D%5C%5CS_%7B660%7D%20%3D%20-1%2C512%2C390)
Hence the sum of the first 660 terms of the sequence is -1,512,390