Help with arithmetic sequence question (1 Viewer)

[MC Squidge]

if the sum of an arithmetic series S_n=n^2+2n

find a formula for T_n, ie the nth term of the series

 

[cookiesandcream]

Tn = 5/2 + (n-1) 5/2 i think?

 

[MC Squidge]

plz explain

 

[Drongoski]

if the sum of an arithmetic series S_n=n^2+2n

find a formula for T_n, ie the nth term of the series

T_n = S_n - S_n-1

= (n² + 2n) - ( (n-1)² + 2(n-1))

= 2n + 1


Is that right ?

 

[Drongoski]

T_n = S_n - S_n-1

= (n² + 2n) - ( (n-1)² + 2(n-1))

= 2n + 1

Is this answer correct ??

 

[MC Squidge]

Is this answer correct ??

dunno. dont have a solution

 

[alakazimmy]

T_n = S_n - S_n-1

= (n² + 2n) - ( (n-1)² + 2(n-1))

= 2n + 1


Is that right ?

Yup.

T₁ = 3. T_n = 2n + 1

So summing all those terms is equivalent to the first term, plus the last term, multiplied by: n/2

So, we have (2n + 4)*n/2 = n² + 2n