Question

the sum of 1st n terms of an A.P is given by Sn=5n^2+3n.Find its nth term.

Answer 1

Sn = n(a1+an)/2 i think might be useful

Answer 2

3,6,9,12

6+3=9,+9=18,+12 = 30

4(3+12)/2 = 2(15) = 30

Answer 3

i know the formula but i don't know what to do
n(a1+an)/2=5n^2+3n???

Answer 4

thats my first instinct :)

Answer 5

5n^2 + 3n = n (5n+3)

2n(5n+3)/2

n(10n+6)/2

Answer 6

when n=1, a1=8

Answer 7

n=2, a1+a2 = 26

8+a2 = 26

a2 = 26-8 = 18

Answer 8

d = a2-a1 = 18-8 = 10

maybe the terms of the sequence are then:

an = 8 + 10(n-1)

Answer 9

n(a1+an)/2=5n^2+3n
n(a1+an)/2=n(5n+3)
(a1+an)/2=5n+3
a1+an=10n+6
an=10n+6-a1???

Answer 10

that looks promising too :)

Answer 11

if a1 = 8 that leaves us:

an = 10n - 2 ; for n>=0

Answer 12

so if your domain starts at 0, an = 10n - 2

if the domain starts at 1 then, an = 10(n-1) + 8

Answer 13

same sequence, different domains

Answer 14

If you have an A.P., with terms
a1 = a
a2 = a + d
a3 = a + 2d
an = a + (n-1)d

then the sum of the first n terms,
Sn = a1 + a2 + ... + an
= n.a + n(n-1)d/2
= (d/2)n^2 + (a-d/2)n

Therefore, if you're given that
Sn = 5n^2 + 3n,

it must be that the coefficients of n^2 and n are equal:
d/2 = 5 --- (1)
a - d/2 = 3 --- (2)

From (1) it follows that d = 10 and hence from (2)
a - 10/2 = 3
i.e., a = 3 + 5 = 8

Therefore the nth term of the underlying series is

an = a + (n-1)d
= 8 + 10(n-1)