Find the general term of the arithmetic sequence where a[4] = 95 a[7] = 110. ?

Question

Find the general term of the arithmetic sequence where  a[4] = 95  a[7] = 110. ?

anonymous · Answer

a[4]=a+3d=95
and a[7]=a+6d=110
solve for both a and d

anonymous · Answer

i'm still confused.

amistre64 · Answer

general term?   is that the same as a common difference?

amistre64 · Answer

or is that spose to be the first term of the seq?

anonymous · Answer

just solve the linear system to get the a and d. 
general term is a[n]=a+(n-1)d

anonymous · Answer

not sure but the answers are 
A. a[n]  = 80 + (n − 1)
B. a[n]  = 5 (n − 1)
C. a[n]  = 80 + 5 (n − 1)
D. a[n]  = 80n
E. None of the above

amistre64 · Answer

we can start at a4, by subtracting 4 from each position

 a[4] = 95  a[7] = 110
  -4             -4
-------------------
  a0 = 95   a3 = 110

amistre64 · Answer

since a arith seq is defined generically as:

an = a0 + d(n-1)

we can fill in the parts now

a3 = 95 + d(3-1) = 110 ;  to find d

anonymous · Answer

a+3d=95
a+6d=110
-----------
     3d=15
=>   d=5
=>   a=95-3*5=80
so a[n]=80+5(n-1)

anonymous · Answer

thank you both <3

amistre64 · Answer

youre welcome, and good luck :)

anonymous · Answer

good luck @laurenbae