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Sagot :
The answer is 286.
Explanation:
We first find the first term of the sequence, a₁. We use the explicit formula for an arithmetic sequence to do this:
[tex]a_n=a_1+d(n-1)[/tex]
We know the 6th term is 22; this means we substitute 6 in for n. We also know the common difference is 6, so we use that for d. That gives us a₆=a₁+6(6-1).
We know the value of the sixth term is 22, so we use that instead of a₆:
22=a₁+6(6-1).
Evaluating this, we have
22=a₁+6(5)
22=a₁+30.
Subtract 30 from both sides, and we have
22-30=a₁
-8=a₁.
We now use this value in our explicit formula:
[tex]a_n=-8+6(n-1)[/tex]
To find the fiftieth term we replace n with 50:
a₅₀= -8+6(50-1)
a₅₀= -8+6(49)
a₅₀= -8+294
a₅₀=286
Explanation:
We first find the first term of the sequence, a₁. We use the explicit formula for an arithmetic sequence to do this:
[tex]a_n=a_1+d(n-1)[/tex]
We know the 6th term is 22; this means we substitute 6 in for n. We also know the common difference is 6, so we use that for d. That gives us a₆=a₁+6(6-1).
We know the value of the sixth term is 22, so we use that instead of a₆:
22=a₁+6(6-1).
Evaluating this, we have
22=a₁+6(5)
22=a₁+30.
Subtract 30 from both sides, and we have
22-30=a₁
-8=a₁.
We now use this value in our explicit formula:
[tex]a_n=-8+6(n-1)[/tex]
To find the fiftieth term we replace n with 50:
a₅₀= -8+6(50-1)
a₅₀= -8+6(49)
a₅₀= -8+294
a₅₀=286
Answer:
286
Step-by-step explanation:
When solving this problem you need to use an explicit formula for an arithmetic sequence to properly answer this question. I hope this helped!❤
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