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Fudgin [204]
2 years ago
9

Given that two terms of an arithmetic sequence are u5 = -3.7 and u15 = -52.3, find the value of the 19th term. ​

Mathematics
1 answer:
Mazyrski [523]2 years ago
4 0

Answer:

  a19 = -71.74

Step-by-step explanation:

The general term of an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 +d(n -1)

The given 5th and 15th terms tell us ...

  -3.7 = a1 +d(5 -1)

  -52.3 = a1 +d(15 -1)

Subtracting the first of these equations from the second, we find ...

  10d = -48.6

  d = -4.86 . . . . . . divide by 10

The 19th term will be ...

  a19 = a1 +d(19 -1)

Subtracting the 15th term from this, we find ...

  a19 -a15 = 4d

  a19 = 4d +a15 = 4(-4.86) +(-52.3)

  a19 = -71.74

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