Problem: Find the sum of the 1st 30 terms: 5+8+11+14...(1st 4 terms shown) How could i make an equation?

Question

Problem: Find the sum of the 1st 30 terms: 5+8+11+14...(1st 4 terms shown) How could i make an equation?

Answer 1

It is an arithmetic series since each number is 3 more than the one before it.  Formula for sum is

S = n/2 (a1 + an) where n = number of terms and a1 is first term while an = the last term

To find the last term use the formula an = a1 + d(n-1) where d = common difference, 3

an = 5 + 3(30 - 1) = 5 + 3(29) = 92

Now plug that into the sum formula

Answer 2

looks to me like sum(5n+3), where n goes 1->30

Split it up into parts:

[sum(5n) for n goes 1->30] + 3*30

[sum(5n) for n goes 1-> 30] + 90

Don't forget  that sum(5n) = 5 * sum(n).

You should probably know a formula for sum(n) for an arbitrary value of 1->n

Answer 3

This is an arithmetic series:

5+(5+3)+(5+2x3)+(5+3x3)+...

Sum to n terms in an arithmetic series

Sn = [n{2a+(n-1)d}] / 2

a - first term of the series, which is 5

n - nth term, 30 in this case

d - common difference, 3 in this case

So, plugging in the values,

Sn = [30{2x5+(29)3}]/2

= 30 {10+87}/2

=15x97

=1455