Which term of the geometric sequence:
2√3, 6,6√3........is 1458 ?
Answers
Answer:
Example 1:
Find the 6th term in the geometric sequence 3,12,48,... .
a1=3, r=123=4a6=3⋅46−1=3⋅45=3072
Example 2:
Find the 7th term for the geometric sequence in which a2=24 and a5=3 .
Substitute 24 for a2 and 3 for a5 in the formula
an=a1⋅rn−1 .
a2=a1⋅r2−1→24=a1ra5=a1⋅r5−1→ 3=a1r4
Solve the firstequation for a1 : a1=24r
Substitute this expression for a1 in the second equation and solve for r .
3=24r⋅r43=24r318=r3 so r=12
Substitute for r in the first equation and solve for a1 .
24=a1(12)48=a1
Example 1:
Find the 6th term in the geometric sequence 3,12,48,... .
a1=3, r=123=4a6=3⋅46−1=3⋅45=3072
Example 2:
Find the 7th term for the geometric sequence in which a2=24 and a5=3 .
Substitute 24 for a2 and 3 for a5 in the formula
an=a1⋅rn−1 .
a2=a1⋅r2−1→24=a1ra5=a1⋅r5−1→ 3=a1r4
Solve the firstequation for a1 : a1=24r
Substitute this expression for a1 in the second equation and solve for r .
3=24r⋅r43=24r318=r3 so r=12
Substitute for r in the first equation and solve for a1 .
24=a1(12)48=a1
Step-by-step explanation:Example 1:
Find the 6th term in the geometric sequence 3,12,48,... .
a1=3, r=123=4a6=3⋅46−1=3⋅45=3072
Example 2:
Find the 7th term for the geometric sequence in which a2=24 and a5=3 .
Substitute 24 for a2 and 3 for a5 in the formula
an=a1⋅rn−1 .
a2=a1⋅r2−1→24=a1ra5=a1⋅r5−1→ 3=a1r4
Solve the firstequation for a1 : a1=24r
Substitute this expression for a1 in the second equation and solve for r .
3=24r⋅r43=24r318=r3 so r=12
Substitute for r in the first equation and solve for a1 .
24=a1(12)48=a1