Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms.
(i) $2, 4, 8, 16, ....$
(ii) $2, \frac{5}{2}, 3, \frac{7}{2}, ...$
(iii) $- 1.2, - 3.2, - 5.2, - 7.2, ...$
(iv) $- 10, - 6, - 2, 2, ...$
(v) $3, 3 + 2, 3 + 22, 3 + 32$
(vi) $0.2, 0.22, 0.222, 0.2222, ....$
(vii) $0, - 4, - 8, - 12, ...$
(viii) $- \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2}, ...$
(ix) $1, 3, 9, 27$
(x) $a, 2 a, 3 a, 4 a, ...$
(xi) $a, a^{2}, a^{3}, a^{4}, ...$
(xii) $2, 8, 18, 32, ...$
(xiii) $3, 6, 9, 12, ...$
(xiv) $1^{2}, 3^{2}, 5^{2}, 7^{2}, ..$
(xv) $1^{2}, 5^{2}, 7^{2}, 73, ..$

Question

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, ....

(ii)

2, \frac{5}{2}, 3, \frac{7}{2}, ...

(iii)

- 1.2, - 3.2, - 5.2, - 7.2, ...

(iv)

- 10, - 6, - 2, 2, ...

(v)

3, 3 + 2, 3 + 22, 3 + 32

(vi)

0.2, 0.22, 0.222, 0.2222, ....

(vii)

0, - 4, - 8, - 12, ...

(viii)

- \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2}, ...

(ix)

1, 3, 9, 27

(x)

a, 2 a, 3 a, 4 a, ...

(xi)

a, a^{2}, a^{3}, a^{4}, ...

(xii)

2, 8, 18, 32, ...

(xiii)

3, 6, 9, 12, ...

(xiv)

1^{2}, 3^{2}, 5^{2}, 7^{2}, ..

(xv)

1^{2}, 5^{2}, 7^{2}, 73, ..

Filo · Accepted Answer

a,b,c are said to be in AP if the common difference between any two consecutive number of the series is same ie b−a=c−b⇒2b=a+c(i) It is not in AP, as the difference between consecutive terms is different.(ii) It is in AP with common difference d=25​−2=21​, tn​=a+(n−1)da=2t5​=2+(5−1)21​Next three terms are 4,29​,5(iii) It is in AP with common difference d=−3.2+1.2=−2 ,and a=−1.2 Next 
three terms are a+(5−1)d=−9.2,a+(6−1)d=−11.2,a+(7−1)d=−13.2(iv) It is in AP with common difference d=−6+10=4, and a=−10Next three
 terms are a+(5−1)d=6,a+(6−1)d=10,a+(7−1)d=14(v) It is in 
AP with common difference d=3+2​−3=2​, anda=3Next 
three terms are a+(5−1)d=3+42​,a+(6−1)d=3+52​,a+(7−1)d=3+62​(vi) It is not in AP since 0.22−0.2=0.222−0.22(vii) It is in AP with common difference d=−4−0=−4 and a=0, Next three 
terms are a+(5−1)d=−16,a+(6−1)d=−20,a+(7−1)d=−24(viii) It is in AP, with common difference 0, therefore next three terms will also be same as previous ones, i.e., −21​(ix) It is not in AP since 3−1=9−3(x) It is in AP with common difference d=2a−a=a and first term is a, Next
 three terms are a+(5−1)d=5a,a+(6−1)d=6a,a+(7−1)d=7a(xi) It is not in AP, as the difference is not constant.(xii) It is in AP with common difference d=2​ and a=2​, Next
 three terms are 
a+(5−1)d=52​=50​,a+(6−1)d=72​,a+(7−1)d=98​(xiii) It is not in AP as difference is not constant.(xiv) It is not in AP as difference is not constant.(xv) It is in AP with common difference d=52−1=24 and a=1,Next three
 terms are a+(5−1)d=97,a+(6−1)d=121,a+(7−1)d=145

Question Text	Which of the following are APs ? If they form an AP, find the common difference $d$ and write three more terms. (i) $2, 4, 8, 16, ....$ (ii) $2, \frac{5}{2}, 3, \frac{7}{2}, ...$ (iii) $- 1.2, - 3.2, - 5.2, - 7.2, ...$ (iv) $- 10, - 6, - 2, 2, ...$ (v) $3, 3 + 2, 3 + 22, 3 + 32$ (vi) $0.2, 0.22, 0.222, 0.2222, ....$ (vii) $0, - 4, - 8, - 12, ...$ (viii) $- \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2}, - \frac{1}{2}, ...$ (ix) $1, 3, 9, 27$ (x) $a, 2 a, 3 a, 4 a, ...$ (xi) $a, a^{2}, a^{3}, a^{4}, ...$ (xii) $2, 8, 18, 32, ...$ (xiii) $3, 6, 9, 12, ...$ (xiv) $1^{2}, 3^{2}, 5^{2}, 7^{2}, ..$ (xv) $1^{2}, 5^{2}, 7^{2}, 73, ..$
Answer Type	Text solution:1
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