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Mazyrski [523]
3 years ago
5

What is the first term of an infinitely decreasing G.P whose sum is 16 and the second term is -0.5?​

Mathematics
1 answer:
Delvig [45]3 years ago
4 0

Answer:

  • 8 + 6√2  

Step-by-step explanation:

<u>Sum of infinite GP is</u>:

  • a/(1 - r) = 16 and

<u>The second term is</u>:

  • ar = -0.5

<u>Eliminate r in the system:</u>

  • a/(1-r) = 16 ⇒  a = 16 - 16r ⇒ 16r = 16 - a ⇒ r = 1 - a/16
  • ar = -0.5 ⇒ r = -0.5/a

<u>Compare the two equations and solve for a:</u>

  • 1 - a/16 = -0.5/a

<u>Multiply both sides by 16a:</u>

  • 16a - a² = -8
  • a² - 16a = 8
  • a² - 16a + 64 = 72
  • (a - 8)² = 72
  • a - 8 = ±√72
  • a = 8 ± √72
  • a = 8 + 6√2  
  • a = 8 - 6√2, excluded as it is negative and makes common difference positive and so an increasing function

a = 8 - 6√2 = -0.4852 ⇒ r = -0.5/a = -0.5/-0.4852 = 1.03 > 1

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