In Execcises 1-6 write the next three terms of the arithmetic sequence. 1. 1,8,15,22,ldots 2. 20,14,8,2,ldots 3. 12,21,30,39,ldots 4. 5,12,19,26,ldots 5. 3,7,11,15,ldots 6. 2,14,26,38,ldots

1. To find the next three terms of the arithmetic sequence $1,8,15,22,\ldots$, we need to determine the common difference between consecutive terms. <br /><br />The common difference is $8 - 1 = 7$. <br /><br />To find the next term, we add the common difference to the last term: $22 + 7 = 29$. <br /><br />To find the term after that, we add the common difference again: $29 + 7 = 36$. <br /><br />Therefore, the next three terms of the sequence are $29, 36, 43$. <br /><br />2. To find the next three terms of the arithmetic sequence $20,14,8,2,\ldots$, we need to determine the common difference between consecutive terms. <br /><br />The common difference is $14 - 20 = -6$. <br /><br />To find the next term, we add the common difference to the last term: $2 + (-6) = -4$. <br /><br />To find the term after that, we add the common difference again: $-4 + (-6) = -10$. <br /><br />Therefore, the next three terms of the sequence are $-4, -10, -16$. <br /><br />3. To find the next three terms of the arithmetic sequence $12,21,30,39,\ldots$, we need to determine the common difference between consecutive terms. <br /><br />The common difference is $21 - 12 = 9$. <br /><br /> the next term, we add the common difference to the last term: $39 + 9 = 48$. <br /><br />To find the term after that, we add the common difference again: $48 + 9 = 57$. <br /><br />Therefore, the next three terms of the sequence are $48, 57, 66$. <br /><br />4. To find the next three terms of the arithmetic sequence $5,12,19,26,\ldots$, we need to determine the common difference between consecutive terms. <br /><br />The common difference is $12 - 5 = 7$. <br /><br />To find the next term, we add the common difference to the last term: $26 + 7 = 33$. <br /><br />To find the term after that, we add the common difference again: $33 + 7 = <br /><br />Therefore, the next three terms of the sequence are $33, 40, 47$. <br /><br />5. To find the next three terms of the arithmetic sequence $3,7,11,15,\ldots$, we need to determine the common difference between consecutive terms. <br /><br />The common difference is $7 - 3 = 4$. <br /><br />To find the next term, we add the common difference to the last term: $15 + 4 = 19$. <br /><br />To find the term after that, we add the common difference again: $19 + 4 = 23$. <br /><br />Therefore, the next three terms of the sequence are $19, 23, 27$. <br /><br />6. To find the next three terms of the arithmetic sequence $226,38,\ldots$, we need to determine the common difference between consecutive terms. <br /><br />The common difference is $14 - 2 = 12$. <br /><br />To find the next term, we add the common difference to the last term: $38 + 12 = 50$. <br /><br />To find the term after that, we add the common difference again: $50 + 12 = 62$. <br /><br />Therefore, the next three terms of the sequence are $50, 62, 74$.