Question

Find an equation for the nth term of the arithmetic sequence.

a15 = -53, a16 = -5

Answer 1

can you find common difference 'd' from that information ?

Answer 2

I don't know how to find it?

Answer 3

These are my options for an answer:

a. an = -725 - 48(n - 1)
b. an = -725 + 48(n + 1)
c. an = -725 + 48(n - 1)
d. an = -725 - 48(n + 1)

Answer 4

How do they get the number -725 and -48?

Answer 5

the common difference 'd' is the difference between consecutive terms!

so, \(\Large a_{16}- a_{15} = d\)

first find d

Answer 6

Oh! d = 48

Answer 7

yes!

Answer 8

a is correct

Answer 9

now u just need 1st term

since we know 15th term, we use the formula
\(\Large a_{15} = a_1 + (15-1)\times 48\)

Answer 10

Okay, thanks. @HARSH123

@hartnn What is a1? How do I do that part?

Answer 11

a_1 is the first term

Answer 12

we already know a15 as -53
so find a_1 from
\(-53 = a_1 +(15-1)\times 48\)

Answer 13

\[-53 = a _{1} + 14 * 48 \]

Answer 14

\[-53 = a _{1} + 672\]

Answer 15

yes, so a1= ... ?

Answer 16

Um. Do I say 672- (-53) = a1?

Answer 17

Oh yes. But that gives me +725

Answer 18

-53 = a1 +672
a1 = -52 -672 = -725

Answer 19

I'm confused, how do I know to make a1's equation negative?

Answer 20

\(-53 = a _{1} + 672 \\ \text{subtracting 672 on both sides} \\ -53 -672 = a_1 \)

a1 was always negative in this case

Answer 21

Ohhhh I see! Thank you so much! So the correct answer is: an = -725 - 48(n - 1)

Answer 22

the formula is \(a_n = a_1 +(n-1)d \\ so, a_n = -725 \large + 48(n-1)\)

Answer 23

option c

Answer 24

You're awesome, thank you :)

Answer 25

and you too are good!
welcome ^_^