t6 + t15 = -141 and the common difference is -7. What is the first term of the sequence?
t6 + t15 = -141
t15 - t6 = -7*9 = -63
2 t15 = -204
t15 = -102
t1 = -102 + 14*7 = -4
The sequence is
-4, -11, -18, -25, -32,
-39, -46, -53, -60, -67,
-74, -81, -88, -95, -102
and the first term is -4.
To find the first term of the arithmetic sequence, you need to use the formula for the nth term of an arithmetic sequence. The formula is:
t(n) = a + (n - 1)d
where:
- t(n) represents the nth term of the sequence
- a represents the first term of the sequence
- d represents the common difference between each term
In this case, you have the following information:
- t(6) + t(15) = -141
- The common difference (d) is -7
Let's plug in these values into the formula and solve for a:
t(6) = a + (6 - 1)(-7)
t(15) = a + (15 - 1)(-7)
Substituting these values into the equation:
(a + 5(-7)) + (a + 14(-7)) = -141
Simplifying the equation:
a - 35 + a - 98 = -141
2a - 133 = -141
2a = -141 + 133
2a = -8
a = -8 / 2
a = -4
Therefore, the first term of the sequence is -4.