Deternine the formula of the nth term of the sequence if the sum of the second and sixth terms of an arithmetic sequence is 4.the third term is 24 more than the leventh tern
a+d + a+5d = 4
2a + 6d = 4 or
a + 3d = 2
a+2d = a+6d + 24
-4d = 24
d = -6
back in a+3d=2
a -18 = 2
a = 20
so term(n) = a + (n-1)(d)
= 20 + (n-1)(-6)
= 20 - 6n + 6
= 26 - 6n
check: according to my formula
term(2) = 26-12 = 14
term(6) = 26-6(6) = -10 , and their sum is 4 , yeahhh
term(3) = 26-6(3) = 8
term(7) = 26-6(7) = -16
is 8 greater than -16 by 24 ? yes, Yeahhh
Owk Reiny would u plz help me understand this"the third term is more dan the 11^th term"what do they mean and what am I supposed 2 do exspecial with the word more
Owk Reiny thank u very much 4 ur help I have found what was confusing me with ur help of corse tnx
To find the formula for the nth term, we need to use the given information about the terms of the sequence.
Let's start by assigning variables:
Let 'a' be the first term of the sequence.
Let 'd' be the common difference between each term of the sequence.
We know that the sum of the second and sixth terms is 4, so we can write the equation:
a + (a + 5d) = 4
Next, we know that the third term is 24 more than the eleventh term. This can be written as:
a + 2d = (a + 10d) + 24
Now, we have two equations with two unknowns. Let's solve them.
From the first equation, we simplify:
2a + 5d = 4
From the second equation, we simplify:
a + 2d = a + 10d + 24
2d = 10d + 24
-8d = 24
d = -3
Substituting the value of d into the first equation:
2a + 5(-3) = 4
2a - 15 = 4
2a = 4 + 15
2a = 19
a = 9.5
Therefore, the first term (a) is 9.5 and the common difference (d) is -3.
Now, we have enough information to find the formula for the nth term of the arithmetic sequence:
An = a + (n - 1)d
Substituting the values:
An = 9.5 + (n - 1)(-3)
An = 9.5 - 3(n - 1)
An = 9.5 - 3n + 3
An = 12.5 - 3n
Hence, the formula for the nth term of the sequence is An = 12.5 - 3n.