The 3 rd term if an arithmetic sequence is 19 and the 9 term is -5 find a and b
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a+2d=19
a+8d=-5
6d=-24
d=-4
a=19-2(-4)=19+8=27
not sure what you u meant about b?
that just all you need to do
check my question above and see if you can help me plz or ask someone you think can help
i guess all our tutors are still sleeping 😂 😂
To find the values of a and b in the arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence:
an = a + (n-1)d
where an is the nth term, a is the first term, n is the term number, and d is the common difference between the terms.
Given that the 3rd term is 19 and the 9th term is -5, we can form two equations using the formula:
a + (3-1)d = 19 -- Equation 1
a + (9-1)d = -5 -- Equation 2
Simplifying Equation 1, we get:
a + 2d = 19
Simplifying Equation 2, we get:
a + 8d = -5
Now, we can solve these two equations simultaneously to find the values of a and b.
Subtracting Equation 1 from Equation 2, we eliminate "a":
(a + 8d) - (a + 2d) = -5 - 19
8d - 2d = -24
6d = -24
d = -4
Now we can substitute the value of d back into Equation 1 to find "a":
a + 2(-4) = 19
a - 8 = 19
a = 19 + 8
a = 27
Therefore, the value of a is 27 and the value of d is -4 in the arithmetic sequence.