Engineering Board Exam Reviewer · Sequences and Series · hard
The sum of an infinite geometric series is 18, and the sum of the squares of its terms is 108. Find the first term.
- 6
- 12
- 3
- 9
Answer
D. 9
Solution
a/1-r=18 a=18(1-r) and a2/1-r2=108. Substituting: 324(1-r)2/(1-r)(1+r)=108 1-r/1+r= 13 r= 12. Then a=18≤ft( 12 )=9.
More Sequences and Series questions
- Find the sum of the first 12 terms of the geometric sequence 3, 6, 12,
- A ball is dropped from a height of 12 m and rebounds to 23 of its previous height after each bounce. What total distance does it travel…
- Express the repeating decimal 0.363636 as a common fraction in lowest terms.
- Insert 4 arithmetic means between 5 and 30. What is the third mean?
- Find the 15th term of the arithmetic sequence 7, 11, 15,
- Solve for x in the following equation: x+4x+7x+·s+64x=1430.
- The seating section in a Coliseum has 30 seats in the first row, 32 seats in the second row, 34 seats in the third row, and so on, until…
- Find the 100th term of the sequence 1.01, 1.00, 0.99,
- Determine x, so that x, 2x+7, 10x-7 will form a geometric progression.
- If one third of the air in a tank is removed by each stroke of an air pump, what fractional part of the total air is removed in 6 strokes?