An arithmetic sequence whose first term is 2 has the property that its second, third, and seventh terms are consecutive terms of a geometric sequence. Determine all possible second terms of the arithmetic sequence.
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Answered question
2020-12-15
An arithmetic sequence whose first term is 2 has the property that its second, third, and seventh terms are consecutive terms of a geometric sequence. Determine all possible second terms of the arithmetic sequence.
Answer & Explanation
l1koV
Skilled2020-12-16Added 100 answers
Step 1
Given:
First of an arithmetic sequence is 2 and has the property that its second, third, and seventh terms are consecutive terms of a geometric sequence.
Step 2
To determine all possible second terms of an arithmetic sequence.
Let, a be the first term of the arithmetic sequence.
And d be the common difference.
So, the terms of the of the arithmetic sequence will be:
That is, to find all possible second terms of the arithmetic sequence. We need to find the value of d.
Step 3
We have that second, third, and seventh terms of an arithmetic sequence are consecutive terms of a geometric sequence.
And second term of an arithmetic sequence is given by,
Therefore, the second of the arithmetic sequence is 4.
Hence, an arithmetic sequence with the first term as 2 and with common ratio as 2 is given by
2, 4, 6, 8,.....