91Ó°ÊÓ

Find the sum of the following APs: (i) \(2,7,12, \ldots\), to 10 terms . (ii) \(-37,-33,-29, \ldots\), to 12 terms. (iii) \(0.6,1.7,2.8, \ldots\), to 100 terms . (iv) \(\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \ldots\), to 11 terms.

Choose the correct choice in the following and justify: (i) 30 th term of the AP: \(10,7,4, \ldots\), is (A) 97 (B) 77 (C) \(-77\) (D) \(-87\) (ii) 11 th term of the \(\mathrm{AP}:-3,-\frac{1}{2}, 2, \ldots\), is (A) 28 (B) 22 (C) \(-38\) (D) \(-48 \frac{1}{2}\)

Write first four terms of the AP, when the first term \(a\) and the common difference \(d\) are given as follows: (i) \(a=10, \quad d=10\) (ii) \(a=-2, \quad d=0\) (iii) \(a=4, \quad d=-3\) (iv) \(a=-1, \quad d=\frac{1}{2}\) (v) \(a=-1.25, d=-0.25\)

For the following APs, write the first term and the common difference: (i) \(3,1,-1,-3, \ldots\) (ii) \(-5,-1,3,7, \ldots\) (iii) \(\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \ldots\) (iv) \(0.6,1.7,2.8,3.9, \ldots\)

Which of the following are APs ? If they form an AP, find the common difference \(d\) and write three more terms. (i) \(2,4,8,16, \ldots\) (ii) \(2, \frac{5}{2}, 3, \frac{7}{2}, \ldots\) (iii) \(-1.2,-3.2,-5.2,-7.2, \ldots\) (iv) \(-10,-6,-2,2, \ldots\) (v) \(3,3+\sqrt{2}, 3+2 \sqrt{2}, 3+3 \sqrt{2}, \ldots\) (vi) \(0.2,0.22,0.222,0.2222, \ldots\) (vii) \(0,-4,-8,-12, \ldots\) (viii) \(-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}, \ldots\) (ix) \(1,3,9,27, \ldots\) (x) \(a, 2 a, 3 a, 4 a, \ldots\) (xi) \(a, a^{2}, a^{3}, a^{4}, \ldots\) (xii) \(\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots\) (xiii) \(\sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12}, \ldots\) (xiv) \(1^{2}, 3^{2}, 5^{2}, 7^{2}, \ldots\) (xv) \(1^{2}, 5^{2}, 7^{2}, 73, \ldots\)

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9 , how many terms are there and what is their sum?

Check whether \(-150\) is a term of the AP: \(11,8,5,2 \ldots\)

Find the 31 st term of an AP whose 11 th term is 38 and the 16 th term is 73 .

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first \(n\) terms.

Find the sum of the first 15 multiples of 8 .