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Sagot :
Answer:
an=5n−35
Step-by-step explanation:
The question says to show the equation in (y=mx+b) form.
So, we convert -30+(n-1)5 into (y=mx+b) form.
we get rid of the parenthesis by multiplying 5 with (n-1)
n×5 = 5n
-1×5=-5
So we are left with -30+5n-5
We solve for like terms, -30-5
so we are left with 5n-35.
an=5n-35
Now we double check if this equation is valid, the question states that the 10th term is 15 and the 14th term is 35. We plug both in, replace of n
10th term is 15
an = 5(10)-35
an = 50-35
an=15 ✔ (that checks out)
14th term is 35
an = 5(14)-35
an = 70-35
an=35 ✔ (that also checks out)
THEREFORE, the equation in (y=mx+b) form would be
an=5n−35
Answer:
- See below
Step-by-step explanation:
Given an AP with:
- a₁₀ = 15
- a₁₄ = 35
General form for nth term:
- aₙ = a₁ + (n - 1)d
Apply this to the given terms:
- a₁ + 9d = 15
- a₁ + 13d = 35
Solve the system above by elimination, subtract the equations:
- 13d - 9d = 35 - 15
- 4d = 20
- d = 5
Find the first term:
- a₁ + 9*5 = 15
- a₁ = 15 - 45
- a₁ = - 30
Now, substitute the values of the first term and common difference into general equation:
- aₙ = a₁ + (n - 1)d
- aₙ = - 30 + (n - 1)*5
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