use your definitions:
a+4d = -12
a+9d = -27
subtract them,
5d = -15
d = -3
back into a+4d = -12
a - 12 = -12
a = 0
check: sequence is 0,-3,-6,-9,-12,-15,-18,-21,-24,-27,-30
yup, we got it
The 5th and 10th terms of a linear sequence are -12 and -27 respectively.Find first term and the common difference of the sequence
2 answers
Linear sequence is other name for arithmetic sequence.
For arithmetic sequence nth term:
an = a1 + ( n - 1 ) d
where:
a1 = initial term of arithmetic progression
d = common difference
In this case:
a5 = a1 + ( 5 - 1 ) d
a5 = a1 + 4 d
a10 = a1 + ( 10 - 1 ) d
a10 = a1 + 9 d
so:
a5 = -12
- 12 = a1 + 4 d
a10 = - 27
- 27 = a1 + 9 d
Now you must solve system:
- 12 = a1 + 4 d
- 27 = a1 + 9 d
Try it.
The solutions are:
a1 = 0
d = - 3
Your sequence:
0 , - 3 , - 6 , - 9 , - 12 , -15 , - 18 , - 21 , - 24 , - 27...
For arithmetic sequence nth term:
an = a1 + ( n - 1 ) d
where:
a1 = initial term of arithmetic progression
d = common difference
In this case:
a5 = a1 + ( 5 - 1 ) d
a5 = a1 + 4 d
a10 = a1 + ( 10 - 1 ) d
a10 = a1 + 9 d
so:
a5 = -12
- 12 = a1 + 4 d
a10 = - 27
- 27 = a1 + 9 d
Now you must solve system:
- 12 = a1 + 4 d
- 27 = a1 + 9 d
Try it.
The solutions are:
a1 = 0
d = - 3
Your sequence:
0 , - 3 , - 6 , - 9 , - 12 , -15 , - 18 , - 21 , - 24 , - 27...