what is the 35th term of an arithmetic sequence where a1=-7 and a18 = 95

Question

amistre64 · Answer

using the formula for an arith seq: an = a1 + d(n-1) , and the given information we can do this.

a18 = -7 +d(18-1)
 95 = -7 +d(17)
102 = d(17)

102/17 = d  in this case,

amistre64 · Answer

a35 = -7 +(102/17)(35-1) = 197

amistre64 · Answer

102/17 reduce to 6 if you wanna make it easier :)

anonymous · Answer

Thank you!

amistre64 · Answer

youre welcome

anonymous · Answer

Wait what if the 1 is lowered down along with the 18...

anonymous · Answer

not to the power of but lowered in the equation if you know what i am talking about

amistre64 · Answer

termed, yes; then a35 becomes a34 and the term that was a36 becomes a35

amistre64 · Answer

so either evaluate the term at a36, or take a35 and add to it

amistre64 · Answer

add 6 to it since that is the common difference between terms

amistre64 · Answer

197 + 6 = 203

a36 = -7 +6(35) = 203

does that make sense?

anonymous · Answer

yes, well i think so. could you help me with one more to make sure i have it?

amistre64 · Answer

i can try :)

anonymous · Answer

thanks :). okay the 27th term of an arithmetic sequence where a(termed 1) =38 and a(termed 17) =-74

amistre64 · Answer

you type out the process as best you can and let me see how your doing

amistre64 · Answer

start out with:  an = a1 + d(n-1) ; and solve for d

anonymous · Answer

Ok wait so I used this equation right?

amistre64 · Answer

or we can solve for d abstractly and then fill in the parts :)

an - a1
------ = d
  n-1


a17 - 38
-------- = d
  17-1


-74 - 38
-------- = d
     16


   -112
-------- = d = -56/8 = -7
     16

amistre64 · Answer

its the standard equation for an arith seq, so yes

anonymous · Answer

Wait the choices i have though are -144, -20.5, -151, and -22.75

amistre64 · Answer

then i suggest we go thru to the end of the solution instead of stopping halfway at -7

amistre64 · Answer

d = -7 is not the same as a27

amistre64 · Answer

an = a1+ d(n-1)

a27 = 38 -7(27-1)
       = 38 -7(26)
       = 38 -182
       = -144

anonymous · Answer

So thatcomes to be -144?

amistre64 · Answer

as long as i did the math in me head right .... yes

anonymous · Answer

Thank you so much!!!!! I get most of them now. Thank you.

amistre64 · Answer

good luck :)

anonymous · Answer

thanks :)