Write a rule for the nth term of the sequence. Use your rule to find a70.
–10, –8, –6, –4, –2, . . .
To find the rule for the nth term of the sequence, we can observe that each term is obtained by adding 2 to the previous term. Therefore, we can express the nth term as:
an = an-1 + 2
Where a1 = -10 (the first term).
Now, to find a70, we can use the formula:
a70 = a69 + 2
To find a69, we can apply the formula again:
a69 = a68 + 2
And so on, until we reach a1.
Substituting the values into the equation, we have:
a69 = a68 + 2
a69 = -2 + 2
a69 = 0
a70 = a69 + 2
a70 = 0 + 2
a70 = 2
Therefore, the 70th term of the sequence is 2.
To find a rule for the nth term of the sequence -10, -8, -6, -4, -2, ..., we can observe that each term is obtained by adding 2 to the previous term. Therefore, the rule for the nth term can be expressed as:
an = -10 + 2(n - 1)
To find a70, we substitute n = 70 into the formula:
a70 = -10 + 2(70 - 1)
= -10 + 2(69)
= -10 + 138
= 128
Hence, a70 is equal to 128.