Question

In terms of n, find the sum of the first n terms of the arithmetic sequence: -4, 5, 14, 23, 32, .....

can you show the steps??

Answer 1

The standard way of writing a sum is \(\Large {n \over 2}(a_1 + a_n)\)

Answer 2

So just substitute a1 with 14, and you're done :)

Answer 3

so n/2 (-4 + 14)

Answer 4

can you explain it to me?

Answer 5

Do you know arithmetic sequence?

Answer 6

ehh kind of, i just want to know how to write it out and solve it

Answer 7

Do you know the relation to find the nth term of an arithmetic sequence?

Answer 8

ahhhh nooo.

Answer 9

Let the nth term be an, d the common difference and a1 be the first term.
\(a_n\) is given as
\[a_n=a_1+(n-1)d\]
Now what's a1 and d here?

Answer 10

a1 is -4 and would be +9

Answer 11

right?

Answer 12

Yeah, you're right:D
Now sum of n terms of a sequence is given by the following
\[S_n=n \times\frac{ (a_1+a_n)}{2}\]

Answer 13

Can you plugin the values and write the relation ?

Answer 14

what would \[a_{n}\] be?

Answer 15

Use the relation that I posted earlier!
\[a_n=a_1+(n-1)d\]

Answer 16

\[a_{n} = -4 + 9n - 9 ?\]

Answer 17

Yeah, you're right
Now plugin this in Sum formula to find sum in terms of n

Answer 18

\[S_{n} = n \times \left(\begin{matrix}-4 -4+9n-9 \\ 2\end{matrix}\right) ?\]

Answer 19

\[S_n=n \times \frac{-4-4+9n-9}{2}\]
Now simplify this:)

Answer 20

Did you understand?

Answer 21

no because i dont know what N is supposed to be

Answer 22

We don't know n here, we have to leave the answer in terms of n. n is the no. of terms for which you want the sum

Answer 23

i still don't understand

Answer 24

Ok, :)
Tell me which part you don't get