Question

Which expression defines the given series for seven terms? 15 + 19 + 23 + . . .

Answer 1

This is an arithmetic series

Answer 2

Do you know the formula for arithmetic series?

Answer 3

oops

Answer 4

it is not +15, I made mistake

Answer 5

it is not +15, I made mistake

Answer 6

\(\large\tt \begin{align} \color{black}{15 + 19 + 23 + . . \\~\\
\implies \color{red}{(}15\color{red}{(} +\color{red}{(}15+4\color{red}{)}+ \color{red}{(}15+2(4)\color{red}{)} + . . \\~\\
\implies \color{red}{(}15\color{red}{)} +\color{red}{(}15+4\color{red}{)}+ \color{red}{(}15+2(4)\color{red}{)} + . . \\~\\
\implies \color{red}{(}15+4(1-1)\color{red}{)} +\color{red}{(}15+4(2-1)\color{red}{)}+ \color{red}{(}15+(4)(3-1)\color{red}{)} + . . \\~\\
\Large \implies \color{red}{(}15+4(n-1)\color{red}{)}
}\end{align}\)

its the nth term

Answer 7

\[\LARGE\color{red}{ \sum_{k=0}^{6}(~~~~~~) }\]

Answer 8

so when k=0 is the first term, and k=1 is second term and on... k=6 is the seventh term.
Sigma is the addition of all of them.

So for k=0,1,2,3,4,

can you think of a pattern/function that generalizes them?

Answer 9

\(\large\tt \begin{align} \color{black}{ \sum_{n=1}^{7}\Large \color{red}{(}15+4(n-1)\color{red}{)}
}\end{align}\)

Answer 10

thats the expression

Answer 11

\[Or,~~~~~\LARGE \sum_{k=0}^{6}~15+4x\]

Answer 12

I think sometimes to make things simpler you have to use index zero.

Answer 13

don't be enslaved to k=1 :P

Answer 14

yes thats also correct

Answer 15

mine is simpler =P

Answer 16

in my expression it should be not x, but k.

Answer 17

i prefer to be natural as natural numbers

Answer 18

lol

Answer 19

I prefer preciseness then:)

Answer 20

@atay085 ???