hi guys , i am troubled with this question
the 8th term of an arithmetic sequence is 25 and the 20th term is -11. find the first term of the sequence and the common difference and use these to write the general term

Question

amistre64 · Answer

you know the 8th and the 20 th terms;

20 - 8 = 12 terms between them, 

25 + 12*d = -11 if i see it right;

amistre64 · Answer

solve for d to determine the "common difference"

amistre64 · Answer

then you would simply resolve for a{1}

a{8} = a{1} + 8(d)  ; they give you a{8} = 25; so solve it for a{1} :)

anonymous · Answer

how to solve for common difference? i really dont get this problem buddy

anonymous · Answer

$$t_8=a+7d=25$$
$$t_{20}=a+19d=-11$$
$$t_{20}-t_8=12d=-36$$
$$d=-3$$
a+7d=25
a-21=25
a=46
the general term
$$t_n=46+((n-1)-3)$$
$$t_n=46-3n+3$$
$$t_n=49-3n$$

amistre64 · Answer

there is a common difference that keeps adding/subtracting to the problem with each iteration; 

spose we start at a{8} and treat it as the first term; 

then a{n} = a{n-1} + d ; 12 times to get to -11

a{12} = a{1} + 12d

-11 = 25 + 12d ; subtract out the 25

-36 = 12d ; now divide out the 12

-3 = d

amistre64 · Answer

the common difference; if I did it right is -3

amistre64 · Answer

Now they want you to solve for the first term; but we already know a{8} = 25

a{8} = a{1} +8(-3)

25 = a{1} - 24 ; add 24

25 + 24 = a{1}

49 = a{1} .. maybe

anonymous · Answer

thank u guys. u are a real life saver