Mathematics: 1. what is the sum of the arithmetic series 2. what is the sum of the first 10 terms of the sequence

1/7= -22/7Step-by-step explanation:...

1. what is the sum of the arithmetic series 2. what

hadilalhjajih

15.01.2022

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

Step-by-step 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:

$S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n$

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:

$a_1=-1,\ d=3,\ n=18\\\\S_{18}=\dfrac{2(-1)+(18-1)(3)}{2}\cdot18=\bigg(-2+(17)(3)\bigg)(9)\\\\=(-2+51)(9)=(49)(9)=441$

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:

$a_1=-1,\ d=2,\ n=10\\\\S_{10}=\dfrac{2(-1)+(10-1)(2)}{2}\cdot10=\bigg(-2+(9)(2)\bigg)(5)\\\\=(-2+18)(5)=(16)(5)=80$

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