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TMUA 2019 · Paper 1 · Question 5 of 20

TMUA 2019 Paper 1 Question 5

Sequences and series — Geometric series · finding the ratio from two sums. Try it first; the answer and a full worked solution are below.

TMUA 2019 · Paper 1Sequences and seriesGeometric series · finding the ratio from two sums6 options
S is a geometric sequence.

The sum of the first 6 terms of S is equal to 9 times the sum of the first 3 terms of S.

The 7th term of S is 360.

Find the 1st term of S.

  1. A4027
  2. B409
  3. C403
  4. D4516
  5. E458
  6. F454
Show the answer and worked solution
answer · E
  1. A4027
  2. B409
  3. C403
  4. D4516
  5. E458
  6. F454
Split the first six terms into the first three plus the next three: the second block is the first block multiplied by r3, so S6 = S3(1 + r3). The condition S6 = 9S3 then gives 1 + r3 = 9, so r3 = 8 and r = 2. (The alternative r = 1 from the algebraic route fails, since it gives S6 = 2S3.) The seventh term is ar6 = 64a = 360, so a = 36064 = 458.