Question

Let \(a_{n}\) be the nth term of an arithmetic sequence. If \(a_{18}\)=26 and \(a_{23}\)=61, which of the following are true?
A. \(a_{14}\)<0
B. \(a_{1}-a_{2}\)<0
C. \(a_{1}+a_{2}+a_{3}+...+a_{27}\)>0

Answer 1

you can surely find a and d from the given info ?

Answer 2

how @@

Answer 3

This type of question i don't know how to do .

Answer 4

You know the nth term of an arithmetic progression /arithmetic sequence/ A.P.

Answer 5

?

Answer 6

wait

Answer 7

a+19d=26
a+24d=61

a=-107
d=7

Answer 8

nop
its a+ (n-1)d

so your eqns will be
a+17d = 26
and
a+ 22d = 61

Answer 9

OMG, messy formula..

Answer 10

a=-93
d=7

Answer 11

right
now it becomes easier to check which ones are true and false ?

Answer 12

let me try

Answer 13

\(a_{14}\)=-2

Answer 14

right

Answer 15

\(a_{2}\)=-86 ?

Answer 16

correct

Answer 17

\(a_{27}\)=89
\[S(27)=(\frac{ (-93+89)\times27 }{ 2 })=-54 ???\]

Answer 18

A and B are correct then ?

Answer 19

yes, bingo!

Answer 20

thank you very much

Answer 21

glad to help