Question

1. What is the sum of the arithmetic series

2. What is the sum of the first 10 terms of the sequence

Answer 1

`\large\boxed{13.\ 441}\\\boxed{14.\ 80}`

Explanation:

You can calculate consecutive terms of the sequence and calculate the sum or use the formula of a sum of terms of an arithmetic sequence:

`S_n=(2a_1+(n-1)d)/(2)\cdot n`

Q13.

`a_n=3n-4\\\\a_1=3(1)-4=3-4=-1\\a_2=3(2)-4=6-4=2\\\\d=a_2-a_1\to d=2-(-1)=2+1=3`

Substitute:

`a_1=-1,\ d=3,\ n=18\\\\S_(18)=(2(-1)+(18-1)(3))/(2)\cdot18=\bigg(-2+(17)(3)\bigg)(9)\\\\=(-2+51)(9)=(49)(9)=441`

Q14.

`a_n=2n-3\\\\a_1=2(1)-3=2-3=-1\\a_2=2(2)-3=4-3=1\\\\d=a_2-a_1\to d=1-(-1)=1+1=2`

Substitute:

`a_1=-1,\ d=2,\ n=10\\\\S_(10)=(2(-1)+(10-1)(2))/(2)\cdot10=\bigg(-2+(9)(2)\bigg)(5)\\\\=(-2+18)(5)=(16)(5)=80`