Find the value of x
a¹=x, d= 3x a9= 25
To find the value of x in this arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1)d
Given:
a₁ = x (first term)
d = 3x (common difference)
a₉ = 25 (ninth term)
We can substitute these values into the formula and solve for x.
a₉ = a₁ + (9 - 1)d
25 = x + (8)(3x)
25 = x + 24x
25 = 25x
x = 1
Therefore, the value of x is 1.
To find the value of x, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the position of the term.
In this case, we are given:
a1 = x
d = 3x
a9 = 25
We can substitute these values into the formula:
a9 = a1 + (9-1)d
Substituting the given values, we have:
25 = x + (9-1)(3x)
Simplifying further:
25 = x + 8(3x)
25 = x + 24x
25 = 25x
Divide both sides by 25 to solve for x:
x = 25/25
x = 1
Therefore, the value of x is 1.
a1+8d=a9
So,
x+8(3x)=25
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