In an arithmetic sequence, we find each term by adding the common difference to the previous term. In the given sequence, the first term is 2 and the common difference is 13. Therefore, to get the second term, we need to add 13 to 2.
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1st Term & & 2nd Term
2 & + 13 ⟶ & 15
We can continue in the same way to find the value of any term in the sequence. Here, we want to find the next three terms after the first term. This means that we will add the common difference 13 to the first term 2, then we will add the common difference 13 to the second term, and so on.
2 + 13 ⟶ 15 + 13 ⟶ 28 + 13 ⟶ 41
We found that the next three terms are 15, 28, and 41.
Alternative Solution
Since this is an arithmetic sequence, the difference between consecutive terms is constant. Therefore, to find the second term, we add the common difference 13 to the first term 2.
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1st Term & & 2nd Term
2 & + 13 ⟶ & 15
To find the third term, we can add the common difference to the first term twice. This means that we can add twice the common difference to the first term.
2 +2( 13) ⟶ 28
Similarly, to get the fourth term, we can add three times the common difference to the first term.
2 +3( 13) ⟶ 41
We obtain that the next three terms are 15, 28, and 41. This is the same answer as before.
