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- Question 1 and 2 Exercise 4.1
- nd infinite sequences\\ 2,4,6,8,…,50 ====Solution==== It is finite sequence whose last term is 50...andinfinitesequences.1,0,1,0,1, \ldots$. ====Solution==== It is infinite sequence, the last term may be... nfinite sequences: ...,−4,0,4,8,…,60 ====Solution==== This is infinite sequence. =====Question 1(i... }{9},-\dfrac{1}{27}, \ldots,-\dfrac{1}{2187}$ ====Solution==== This finite sequence. =====Question 2(i)====
- Question 1 Exercise 4.5
- i)===== Compute the sum 3+6+12+…+3.29 ====Solution==== In the given geometric series: a1=3,...Computethesum8+4+2+\ldots+\dfrac{1}{16}$ ====Solution==== In the give geometric series $$a_1=8, \quad r... = Compute the sum 24+25+26+…+210 ====Solution==== In the give geometric series.\\ $$a_1=2^4, \q... sum 85,−1,58,…, ====Solution==== Here a1=85 \begin{align}r&=\d
- Question 3 and 4 Exercise 4.1
- rac{2}{3} \dfrac{3}{4}, \dfrac{4}{5}, \ldots$ ====Solution==== We can reform the given sequence to pick the ... gested by the pattern. 2,−4,6,−8,10,… ====Solution==== We can reform the given sequence to pick the ... suggested by the pattern. 1,−1,1,−1,… ====Solution==== We can reform the give sequence to pick the p... efined recursively. a1=3, an+1=5−an. ====Solution==== Given a1=3,an+1=5−an. For n=1 \be
- Question 12 & 13 Exercise 4.2
- ry during his twenty first year of work? GOOD ====Solution==== Suppose a1 represents salary of worker at ... e arithmetic mean between 12 and 18. GOOD ====Solution==== Here a=12,b=18.\\ Let say A be arithmeti... an between 13 and 14. ====Solution==== Here a=13,b=14,\\ Let ... d the arithmetic mean between −6,−216. GOOD ====Solution==== Here a=−6,b=−216.\\ Let A be arithmetic
- Question 5 Exercise 4.1
- eries in expanded form, ∑6j=1(2j−3) ====Solution==== \begin{align}\sum_{j=1}^6(2 j-3)&=(2.1-3)+(2.... n expanded form, ∑5k=1(−1)k2k−1 ====Solution==== \begin{align}\sum_{k=1}^5(-1)^k 2^{k-1}& =(-1... ed form, ∑∞j=112j ====Solution==== \begin{align}\sum_{j=1}^{\infty} \dfrac{1}{2^... um_{k=0}^{\infty}\left(\dfrac{3}{2}\right)^k$ ====Solution==== \begin{align}\sum_{k=0}^{\infty}\left(\dfrac{
- Question 2 Exercise 4.3
- one that is missing: a1=2,n=17,d=3. GOOD ====Solution==== Given: a1=2,n=17,d=3 \\ We need to find ... that are missing a1=−40,S21=210. GOOD ====Solution==== Given: a1=−40 and S21=210.\\ So we ha... that are missing a1=−7,d=8,Sn=225. GOOD ====Solution==== Given: a1=−7,d=8,Sn=225, we have to fin... ne that are missing: an=4,S15=30. GOOD ====Solution==== Given: an=4,S15=30.\\ Thus we have $n=
- Question 1 Exercise 4.4
- ic ric sequence given that a1=5,r=3 ====Solution==== The gcometric sequence is a1,a1r,a1r...ncegiventhata_1=8, \quad r=-\dfrac{1}{2}$ ====Solution==== The geomerric sequence is a1,a1r,a1r...ta_1=-\dfrac{9}{16}, \quad r=-\dfrac{2}{3}$ ====Solution==== The geometric sequence is a1,a1r,a1r...hata_1=\dfrac{x}{y}, \quad r=-\dfrac{y}{x}$ ====Solution==== The geometric sequence is, $a_1, a_1 r, a_1 r
- Question 8 Exercise 4.4
- Find the geometric mean of 3.14 and 2.71 ====Solution==== Here a=3.14 and b=2.71\\ then $$G= \pm \s... == Find the geometric mean of −6 and −216 ====Solution==== Here a=−6 and b=−216 then\\ \begin{align}... == Find the geometric mean of x+y and x−y ====Solution==== Here a=x+y and b=x−y\\ then $$G= \pm \sqr... ometric mean of √2+3 and √2−3 ====Solution==== Here a=√2+3 and \begin{align}b&=\sqrt
- Question 4 Exercise 4.5
- decimal to common fraction 0.¯8 ====Solution==== We can write $$0 . \overline{8}=0.888888 \ldo... ecimal to common fraction 1.¯63 ====Solution==== Since \begin{align}1 . \overline{63}&=1+0.63+... ecimal to common fraction 2.¯15 ====Solution==== Since \begin{align}2 . \overline{15}&=2+0.15+... cimal to common fraction 0.¯123 ====Solution==== Since $$0 . \overline{123}=0.123+0.000123 +0.
- Question 6 Exercise 4.1
- using its general recursive definition. GOOD ====Solution==== For n=5, we have Pascal sequence as follow... 6$ by using its general recursive definition. ====Solution==== As we know the general definition of Pascal s... $ by using its general recursive definition. =====Solution===== As we know the general definition of Pascal
- Question 2 Exercise 4.5
- re missing a1=1,r=−2,an=64. ====Solution==== We first find n and then Sn\\ We know a...thataremissingr=\dfrac{1}{2}, a_9=1, n=9$ ====Solution==== We first find a1 and then S9.\\ We kno... nes that are missing r=−2,Sn=−63,an=−96 ====Solution==== We know that\\ \begin{align}S_n&=\dfrac{a_1(r
- Question 1 and 2 Exercise 4.2
- the arithmetic sequence 2,5,8,… GOOD ====Solution==== Here a1=2, d=5−2=3 and n=15. We know t... and the 21st is 108. Find the 7th term. GOOD ====Solution==== Since a1=8 and a21=108. We know that
- Question 3 and 4 Exercise 4.2
- arithmetic progression 6,9,12,…,78. ====Solution==== Here a1=6 and d=9−6=3 and an=78.\\ We... ithmetic progression. Also find its 7th term. ====Solution==== Given that an=2n+7.−−−(1) Then \begin
- Question 5 and 6 Exercise 4.2
- , \ldots$$ is an A.P. Also find its nth term. ====Solution==== We first find nth term. Each term of the se... k-4$ are in A.P. Also find the sequence. GOOD ====Solution==== Since the given terms are in A.P, \begin{alig
- Question 14 Exercise 4.2
- three arithmetic means between 6 and 41. GOOD ====Solution==== Let A1,A2,A3 be three arithmetic means... four arithmetic means between 17 and 32. GOOD ====Solution==== Let A1,A2,A3,A4 be four arithmetic m