The sum of two consecutive terms of the sequence: ;
is 308. Determine the two terms.

Question

The sum of two consecutive terms of the sequence: $$ 21 ; 35 ; 49 $$; is 308. Determine the two terms.

UpStudy AI · Accepted Answer

The given sequence is:
$$ 21, \, 35, \, 49, \, 63, \, 77, \, \ldots $$

This is an **arithmetic sequence** where each term increases by a common difference $$ d = 14 $$.

Let's denote the two consecutive terms as $$ x $$ and $$ x + 14 $$.

According to the problem, their sum is 308:
$$
x + (x + 14) = 308
$$
$$
2x + 14 = 308
$$
$$
2x = 308 - 14
$$
$$
2x = 294
$$
$$
x = 147
$$

So, the two consecutive terms are:
$$
147 \quad \text{and} \quad 161
$$

**Verification:**
$$
147 + 161 = 308
$$
These terms also fit into the given arithmetic sequence.

**Answer:**  
The two consecutive terms are 147 and 161.
The two consecutive terms are 147 and 161.

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