Determine the missing values to logically complete the given numerical sequence.

Answer:In the sequence

3, 8, 18, 38, 【78】, 158, 【318】

, the first missing term is 【78】 and the second missing term is 【318】.

The first missing term is 78 and the second missing term is 318.

The pattern governing the sequence can be defined recursively as

a_{n+1} = 2a_n + 2

. Following

38

, the term is

(38 \times 2) + 2 = 78

. Following

158

, the term is

(158 \times 2) + 2 = 318

. Alternatively, observing the difference between consecutive terms shows

+5, +10, +20, +40, +80, +160

, yielding

38 + 40 = 78

and

158 + 160 = 318

Analyze the rule connecting consecutive terms in the sequence

Each term is generated by multiplying the preceding term by

2

and adding

2

(3 \times 2) + 2 = 8

(8 \times 2) + 2 = 18

, and

(18 \times 2) + 2 = 38

. Alternatively, the differences between successive terms double each step (

+5, +10, +20, \dots

Identifying the mathematical operational relationship allows computing unknown terms.

Calculate the value for the first blank following

38

(38 \times 2) + 2 = 76 + 2 = 78

(or

38 + 40 = 78

Applying the identified rule to

38

yields the first missing term.

Verify the calculated value against the given term

158

(78 \times 2) + 2 = 156 + 2 = 158

(or

78 + 80 = 158

Ensures consistency across the pattern before proceeding to the final term.

Calculate the value for the second blank following

158

(158 \times 2) + 2 = 316 + 2 = 318

(or

158 + 160 = 318

Applying the operational rule to

158

yields the second missing term.

Mixed Arithmetic Series and Double Difference Progression

Estimated Time:1m 15s

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