Problem

Find a1 and Sn for a geometric sequence with the values given below.
r=12,an=1132,n=6
a1=11 (Simplify your answer.)
Sn= (Simplify your answer.)

Answer

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Answer

So, the first term of the geometric sequence is 11 and the sum of the first 6 terms is 23132.

Steps

Step 1 :Given that the common ratio r=12, the nth term an=1132, and n=6.

Step 2 :We can find the first term a1 of the geometric sequence using the formula a1=anrn1.

Step 3 :Substituting the given values into the formula, we get a1=11/32(1/2)61.

Step 4 :Solving the above equation, we find that a1=11.

Step 5 :We can find the sum Sn of the first n terms of the geometric sequence using the formula Sn=a1(1rn)1r.

Step 6 :Substituting the given values into the formula, we get Sn=11(1(1/2)6)1(1/2).

Step 7 :Solving the above equation, we find that Sn=23132.

Step 8 :So, the first term of the geometric sequence is 11 and the sum of the first 6 terms is 23132.

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