The sixth term of GP is 16 and the third term is 2.Find the first term and common ratio. 6th term =16 3rd term=2 So ar^5=16 and ar^2=2, then divide. So r^3=8, and r^3 =2^3. Therefore r =2 and a=1/2
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Looks good to me.
The formula of the GP
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The 3rd term of a geometric profession is 16, while the 6th term of the same go is 2 find the first term
Let's use the formula for the nth term of a geometric sequence:
a₃ = a * r²
a₆ = a * r⁵
We can use these equations to create a system of equations:
16 = a * r²
2 = a * r⁵
We can solve for the first term (a) by isolating it in one of the equations:
a = 16 / r²
Substituting this expression for a into the second equation:
2 = (16 / r²) * r⁵
Simplifying:
2 = 16r³
r³ = 1/8
r = 1/2
Now we can find the first term:
16 = a * (1/2)²
16 = a * 1/4
a = 64
Therefore, the first term of the geometric sequence is 64.
a₃ = a * r²
a₆ = a * r⁵
We can use these equations to create a system of equations:
16 = a * r²
2 = a * r⁵
We can solve for the first term (a) by isolating it in one of the equations:
a = 16 / r²
Substituting this expression for a into the second equation:
2 = (16 / r²) * r⁵
Simplifying:
2 = 16r³
r³ = 1/8
r = 1/2
Now we can find the first term:
16 = a * (1/2)²
16 = a * 1/4
a = 64
Therefore, the first term of the geometric sequence is 64.
3 answers