Question

Find the missing terms of the arithmetic sequence ...,27,?,?,?,53,... Show each step of the process clearly

Answer 1

Answer:

Step-by-step explanation:

Looking at the arithmetic sequence, the 4th term is 27 the 8th term is 53. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

Therefore, the 4th term, T4 will be

27 = a + (4 - 1) d

27 = a + 3d - - - - - - - - 1

The 8th term, t8 would be

53 = a +(8 - 1) d

53 = a + 7d - - - - - - - - -2

Subtracting equation 1 from equation 2, it becomes

- 26 = - 4d

d = - 26/- 4 = 6.5

Substituting d = 6.5 into equation 1, it becomes

53 = a + 7 × 6.5

53 = a + 45.5

a = 53 - 45.5 = 7.5

The missing terms are

7.5, 14, 20.5, 27, 33.5, 40, 46.5, 53