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301. If the sum of first 7 terms of an A .P. is 49 and that of first 17 terms is 289, find the sum of first n terms.

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302. If S_n, the sum of first n terms of an A .P. is given by S_n = 3n² – 4n, then find its n^thterm.

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303.

If S_n, the sum of first n terms of an A .P. is given by S_n = 5n² + 3n, then find its n^thterm.
S_n = 5n² + 3n

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304. Find the sum of the :
First 25 terms of an A .P. whose nth term is given by a_n= 7 – 3n. z

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305.

Find the sum of the :
(i) First 25 terms of an A .P. whose nth term is given by a_n= 7 – 3n

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306. The sum of n terms of 2 A .P.’s sire in the ratio 7n + 1 : 4n + 27, show that the ratio of their 11th term is 4 : 3.

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307. If the sum of m terms of an A .P. is the same as the sum of its nth terms. Show that the sum of its (m + n)th terms is zero.

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308. If S₁, S₂,S₃, be the sum of n, 2n and 3n terms S₃ = 3(S₁ – S₁).

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Let ‘a’ be the first term and d the common difference of the A .P.

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310.

If in sin A .P. the sum of m terms is equal to n and the sum of n terms is equal to m, then prove that the sum of (m + n) terms is –(m + n).

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