7. If $t_{3} = 20$ and $t_{20} = 122$ then the common difference is
A. 102
B. 6
C. 6.375
D. 17

Answer

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Answer

\boxed{d = 6}

Steps

Step 1 ：Given the 3rd term ( $t_{3}$ ) and the 20th term ( $t_{20}$ ) of an arithmetic sequence, we can write the arithmetic sequence formula: $t_{n} = a + (n - 1) d$

Step 2 ：Using the given values, we have two equations: $t_{3} = a + 2 d = 20$ and $t_{20} = a + 19 d = 122$

Step 3 ：Solve the system of linear equations to find the value of d

Step 4 ：\boxed{d = 6}

7. If t3=20 and t20=122 then the common difference isA. 102B. 6C. 6.375D. 17

Answer

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7. If $t_{3} = 20$ and $t_{20} = 122$ then the common difference is
A. 102
B. 6
C. 6.375
D. 17