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the fourth term of the geometric progression
is 6 and the Seventh term
is -48. Calculate
Common ratio,the first term and the sum of the first eleven terms​

Sagot :

sqdancefan

9514 1404 393

Answer:

  • common ratio: -2
  • first term -3/4
  • sum of 11 terms: -2049/4

Step-by-step explanation:

The formula for the generic term can be solved to find the first term and the common ratio.

  an = a1·r^(n-1)

For the given terms, we have ...

  a4 = 6 = a1·r^(4 -1)

  a7 = -48 = a1·r^(7-1)

Dividing the second equation by the first gives ...

  a7/a4 = -48/6 = r^(6 -3)

  r = (-8)^(1/3)

  r = -2 . . . . . . . . . . the common ratio

Then the first term is ...

  6 = a1·(-2)^(3) = -8a1

  -6/8 = a1 = -3/4 . . . . . the first term

__

The sum of N terms is ...

  Sn = a1·(r^n -1)/(r -1)

Then the sum of 11 terms is ...

  S11 = (-3/4)((-2)^11 -1)/(-2-1) = (-1/4)(2^11 +1)

  S11 = -2049/4 . . . . . the sum of 11 terms

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