If the fifth term of an arithmetic sequence is −5 and the ninth term is −17, the first term of this sequence must be?
Would it be 7?

Question

If the fifth term of an arithmetic sequence is −5 and the ninth term is −17, the first term of this sequence must be?
Would it be 7?

kc_kennylau · Answer

The $n$th term of an arithmetic sequence is $a+d\times(n-1)$, where $a$ is the first term and $d$ is the common difference

kc_kennylau · Answer

Try to set up two equations from that :)

anonymous · Answer

how would  I do that if I don't have the first term nor the second term to find the common difference?

kc_kennylau · Answer

You set up two equations to find that

kc_kennylau · Answer

The first equation is $a+d\times(5-1)=-5$

kc_kennylau · Answer

Can you figure out the second equation by yourself? :)

nikato · Answer

Sooty to intrude. But I got 7 too

anonymous · Answer

a+d X ( 9-1) = -17?

anonymous · Answer

oh really? I was just guessing on that haha

kc_kennylau · Answer

exactly

kc_kennylau · Answer

now you have a system of equations:
$$\left\{\begin{array}{lr}a+4d=-5&---(1)\a+8d=-17&---(2)\end{array}\right.$$

anonymous · Answer

ohhh not this thing haha ok

anonymous · Answer

I got 7?

kc_kennylau · Answer

yep :)
$$2\times(1)-(2):a=7$$

anonymous · Answer

Thank you. You are the best

kc_kennylau · Answer

Thanks <3