In an A.P., the 4th term is 11 and the sum of the 5th and 7th terms is 34. Find the first term and the common difference, write the first four terms, and check whether 150 is a term of this A.P.

Q.5 (i) In an A.P., the 4th term is 11 and the sum of the 5th and 7th terms is 34. Find the first term and the common difference, write the first four terms, and check whether 150 is a term of this A.P.

Doubtly AI Asked 27 Oct 2026 AI-generated · not yet verified ssc 10th Save WhatsApp Report

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Answer: \(a = 2,\ d = 3\); A.P. is 2, 5, 8, 11, ...; 150 is not a term.

\(t_4 = a + 3d = 11\) ...(I)

\(t_5 + t_7 = (a + 4d) + (a + 6d) = 2a + 10d = 34\), so \(a + 5d = 17\) ...(II)

Subtracting (I) from (II): \(2d = 6\), so \(d = 3\) and \(a = 11 - 9 = 2\).

The A.P. is 2, 5, 8, 11, ...

If 150 is the \(n\)th term: \(2 + (n - 1)3 = 150 \Rightarrow 3(n - 1) = 148 \Rightarrow n - 1 = \dfrac{148}{3}\), which is not a whole number. So 150 is not a term of this A.P.

Doubtly AI · 27 Oct 2026 AI-generated · not yet verified Report

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In an A.P., the 4th term is 11 and the sum of the 5th and 7th terms is 34. Find the first term and the common difference, write the first four terms, and check whether 150 is a term of this A.P.

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