First Year Math Sequences and Series

$2. Sum the seriesii) \frac{3}{\sqrt{2}}+2 \sqrt{2}+\frac{5}{\sqrt{2}}+\ldots .+a_{13}$

$18. The sum of the first n terms of two A.P.s are as 13-7 n: 3 n+1 . Find the ratio of their first terms and also of their second terms.$

$3. A man borrows Rs. 1100 and agree to repay with a total interest of Rs. 230 in 14 installments each installment being less than the preceding by Rs. 10 . What should be his first installment?$

$11. What distance will a ball travel before coming to rest if it is dropped from a height of 75 meters and after each fall it rebounds \frac{2}{5} of the distance it fell?$

$8. If S_{2} S_{3} S_{5} are the sums of 2 n 3 n 5 n terms of an A.P. show that S_{5}=5\left(S_{3}-S_{2}\right)$

$Q.35 The common ratio of a geometric sequence cannot be(a) 3(b) 1(c) 2(d) 0$