Question

Find the first term, the common difference, and tn for a series having Sn = 3n2+5n.

Answer 1

Answer: T1 = 8   D = 6  Tn = 6n+2

Step-by-step explanation:

We know the Sum of N terms(Sn) = 3n^2+5n

So the sum of only the first term would equal the first term

So...

T1 = 3 * 1^2 + 5*1 = 3 + 5

T1 = 8

Now to find the difference we could use the equation to find the second term.

We first need to find the sum of the first and the second terms

S2 = 3*2^2 + 5*2 = 3*4 + 5*2 = 12 + 10 = 22

Now to find the second term, we just subtract the first term from the sum

T2 = 22 - 8

T2 = 14

To find D(Difference) we just subtract the first term from the second term

D = T1 - T2 = 14 - 8

D = 6

So now we just need to find Tn.

Tn = 6n+2