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If the seventh term of an AP is equal to 11times the eleventh term.find the 18th term of the Ap, given that the common difference is 5.

"seventh term of an AP is equal to 11times the eleventh term"

a + 6d = 11(a + 10d)
a + 6d = 11a + 110d
10a = -104d

but d = 5, so
10a = -520
a = -52

term(18) = a + 17d = ....

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In an Arithmetic Progression (AP), where each term differs from the previous one by a constant called the common difference, we can easily find the nth term using a formula: nth term = first term + (n-1) * common difference. In the given scenario, the seventh term of the AP is equal to 11 times the eleventh term. By plugging in the values, we can find the value of the first term: 7th term = first term + (7-1) * common difference = first term + 6 * 5 = first term + 30. Therefore, 11 times the eleventh term is equal to first term + 30, from which we can calculate the value of the first term. With the first term and common difference known, we can now find the 18th term of the AP by using the formula mentioned earlier: 18th term = first term + (18-1) * common difference. By substituting the values, the 18th term of the AP can be determined as well.