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The seventh term of an AP is four times its second term and twelfth term is 2 more than three times of its fourth term .find AP?
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The seventh term of an AP is four times its second term and twelfth te...



Given:
- The seventh term of an AP is four times its second term.
- The twelfth term is 2 more than three times of its fourth term.

Let's find the AP:

Finding the AP:
- Let the second term of the AP be 'a' and the common difference be 'd'.
- The seventh term of the AP is given as 4a (since it is four times the second term).
- Therefore, the seventh term is a + 6d = 4a.
- Solving the above equation, we get d = a/3.
- The fourth term of the AP is a + 3d.
- The twelfth term of the AP is a + 11d = 3(a + 3d) + 2 (since it is 2 more than three times the fourth term).
- Substituting the value of d, we get a + 11(a/3) = 3(a + a/3) + 2.
- Solving the above equation, we get a = 3.
- Therefore, the common difference, d = a/3 = 1.
- Hence, the AP is 3, 4, 5, 6, 7, ...

Conclusion:
- The AP is 3, 4, 5, 6, 7, ...

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The seventh term of an AP is four times its second term and twelfth term is 2 more than three times of its fourth term .find AP?
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