Reference no: EM131000097
1. Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an find a7, the seventh term of the sequence.
1. 1.5, -3, 6, -12, ....
2. 5, -1, 1/5, -1/25, ....
2. Use the formula for the sum of the first n terms of a geometric sequence to solve -
i. find the sum of the first 11 terms of the geometric sequence:
3, -6, 12, -24, ....
ii. find the sum of the first 11 terms of the geometric sequence:
4, -12, 36, -108, ....
3. A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying statement Sk+1 completely.
1. Sn: 2+7+12+...+(5n-3) = n(5n-1)/2.
2. Sn: 2 is a factor of n2 - n +2.
4. Use mathematical induction to prove that each statement is true for every positive integer n.
1. 3+7+11+ ...+ (4n-1) = n(2n+1)
2. 2+7+12+...+(5n-3) = n(5n-1)/2.
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