Class 10

Math

All topics

Arithmetic Progressions

What is the sum of the first nineteenth terms of the arithmetic sequence 2, 6, 10, 14.....?

- $522$
- $622$
- $722$
- $822$

The sum of n terms of an arithmetic sequence can be calculated by $S_{n}=2n [2a+(n−1)d]$

Where, n denotes the total number of terms

$a$= first term

$d=$common difference

$S_{n}$ = Sum of n terms

$∴a=2d=4n=19$Where, n denotes the total number of terms

$a$= first term

$d=$common difference

$S_{n}$ = Sum of n terms

$S=2n [2×a+(n−1)d]$

$S=219 [2×2+(19−1)4]$

$S=219 [4+72]$

$S=9.5[76]$

$S=722$