what is S19 for the arithmetic series 2+9+16+23+...?

Question

jim_thompson5910 · Answer

S19 means "find the sum of the first 19 terms"

jim_thompson5910 · Answer

So you could painstakingly generate the first 19 terms, then add up them, but there's a much easier way

jim_thompson5910 · Answer

we'll need the first term and the common difference

first term: a1 = ???
common difference: d = ???

emilyjones284 · Answer

a1=2 and d=7

jim_thompson5910 · Answer

so the nth term is 

an = a1 + d(n-1)

an = 2 + 7(n-1)

an = 2 + 7n - 7

an = 7n - 5

jim_thompson5910 · Answer

You use the first term (a1), the nth term (an) and the number of terms (n) to calculate Sn (the sum of the first n terms)

jim_thompson5910 · Answer

By this formula

Sn = n(a1 + an)/2

emilyjones284 · Answer

wait im confused why do i need the first 5 terms?

jim_thompson5910 · Answer

that -5 doesn't mean the first 5 terms

jim_thompson5910 · Answer

an = 7n - 5 helps you find any term you want

say the 3rd term, so n = 3

an = 7n - 5

a3 = 7*3 - 5 ... plug in n = 3

a3 = 21 - 5

a3 = 16

surely enough, 16 is indeed the 3rd term

emilyjones284 · Answer

ohhhh never mind I misread something sorry

jim_thompson5910 · Answer

that's ok

jim_thompson5910 · Answer

use this formula

Sn = n(a1 + an)/2

to find S19

jim_thompson5910 · Answer

In this case,

a1 = 2
an = 7n - 5 (just found this)
n = 19

emilyjones284 · Answer

so is s19=128 correct?