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First Year Math Sequences and Series


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Class 9Class 10First YearSecond Year
1.Sumtheseries.(b)7+77+777+7777+tonterms1. Sum the series.(b) 7+77+777+7777+\ldots to n terms

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

2.Sumtheseriesii)32+22+52+.+a132. 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.
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.

18.ThesumofthefirstntermsoftwoA.P.sareas137n:3n+1.Findtheratiooftheirfirsttermsandalsooftheirsecondterms.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?
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?

3.AmanborrowsRs.1100andagreetorepaywithatotalinterestofRs.230in14installmentseachinstallmentbeinglessthantheprecedingbyRs.10.Whatshouldbehisfirstinstallment?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?
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?

11.Whatdistancewillaballtravelbeforecomingtorestifitisdroppedfromaheightof75metersandaftereachfallitrebounds25ofthedistanceitfell?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)
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)

8.IfS2S3S5arethesumsof2n3n5ntermsofanA.P.showthatS5=5(S3S2)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
Q.35 The common ratio of a geometric sequence cannot be(a) 3(b) 1(c) 2(d) 0

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

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