Question

identify the 33rd term of the arthmetic sequence 9, 7 1/2, 6

Answer 1

\(\Large \color{purple}{\rightarrow 9{1 \over 2} - (n)({1 \over 2}) }\)

Substitute n with 33.

Answer 2

the general formula for an arithmetic sequence is:\[a_n=a_1+d(n-1)\]

Answer 3

@amistre64 Yes, I just simplified the formula and added that 1/2 to 9.

Answer 4

they give you a1, they give you n=33

the only thing to do is figure out the common difference (d) between each term.

Answer 5

yes, but the real question stems from not knowing how to do these things in general.

Answer 6

answers -39 thanks for your help

Answer 7

the common difference can be determined simply by subtracting 2 terms that are side by side: a2-a1 is the simplest way to me: 7 1/2 - 9 = -1 1/2

\[a_{33}=9-\frac{3}{2}(33-1)\]

Answer 8

im trying to see how Parth got that setup :)

Answer 9

-39 is correct; but i cant get that with your setup ... is there a typo?

Answer 10

\(\Large \color{purple}{\rightarrow 9 - (n -1)({1 \over 2}) }\)

\(\Large \color{purple}{\rightarrow 9 - {(n - 1) \over 2} }\)

\(\Large \color{purple}{\rightarrow {18 - (n - 1) \over 2} }\)

\(\Large \color{purple}{\rightarrow {18 - n + 1 \over 2} }\)

\(\Large \color{purple}{\rightarrow {19 - n \over 2} }\)

\(\Large \color{purple}{\rightarrow 9.5 - {n \over 2} }\)

Simplified. @amistre64 Can I please please please have a medal?

Answer 11

I'm sorry about asking for the medal, but still am I right?

Answer 12

33/2 = 16.5

-16.5
9.5
------
- 7.0 which is not= -39

Answer 13

the common difference is not -1/2, is where your error is creeping in at

Answer 14

See it Oh lol it's 3/2

Answer 15

other than that, your simplification would have been sufficient

Answer 16

\(\Large \color{purple}{\rightarrow 10.5 - {3n \over 2} }\)

Answer 17

\(\Large \color{purple}{\rightarrow 10.5 - 49.5 }\)

\(\Large \color{purple}{\rightarrow -39 }\)