Q. 104.8( 6 Votes )

# Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

Answer :

(i)

Common difference, d_{1} = 6 – 3 = 3

Common difference, d_{2}= 12 – 6 = 6

Since, d_{1} ≠ d_{2}

Therefore, it’s not an A.P.

Common difference, d_{1} = -4 – 0 = -4

Common difference, d_{2}= -8 – (-4) = - 4

Since, d_{1} = d_{2}

Therefore, it’s an A.P. with common difference, d = -4

Common difference, d_{1}= - =

Common difference, d_{2} = - =

Since, d_{1} ≠ d_{2}

Therefore, it’s not an A.P.

Common difference, d_{1}= 2 – 12 = -10

Common difference, d_{2}= -8 -2 = -10

Since,d_{1} = d_{2}

Therefore, it’s an A.P. with common difference, d = -10

Common difference, d_{1}= 3 – 3 = 0

Common difference, d_{2}= 3 – 3 = 0

Since, d_{1}=d_{2}

Therefore, it’s an A.P. with common difference, d = 0

Common difference, d_{1}= p + 90 – p = 90

Common difference, d_{2}= p + 180 – p – 90 = 90

Since, d_{1}=d_{2}

Therefore, it’s an A.P. with common difference, d = 90

Common difference, d_{1}= 1.7 – 1.0 = 0.7

Common difference, d_{2}= 2.4 – 1.7 = 0.7

Since, d_{1}=d_{2}

Therefore, it’s an A.P. with common difference, d = 0.7

Common difference, d_{1}= -425 + 225 = -200

Common difference, d_{2}= -625 + 425 = -200

Since, d_{1}=d_{2}

Therefore, it’s an A.P. with common difference, d = -200

Common difference, d_{1}= 10 + 2^{6} – 10 = 2^{6} = 64

Common difference, d_{2} = 10 + 2^{7} – 10 – 2^{6} = 2^{6} (2 – 1) = 64

Since, d_{1}=d_{2}

Therefore, it’s an A.P. with common difference, d = 64

Common difference, d_{1} = (a + 1) + b – a – b = 1

Common difference, d_{2} = (a + 1) + (b + 1) – (a + 1) – b = 1

Since, d_{1} = d_{2}

Therefore, it’s an A.P. with common difference, d = 1

Common difference, d_{1}= 3^{2} – 1^{2} = 8

Common difference, d_{2} = 5^{2} – 3^{2} = 25 – 9 = 16

Since, d_{1}≠d_{2}

Therefore, it’s not an A.P.

Common difference, d_{1} = 5^{2} – 1^{2} = 24

Common difference, d_{2} = 7^{2} – 5^{2} = 24

Since, d_{1} = d_{2}

Therefore, it’s an A.P. with common difference, d = 24

Rate this question :

Find the indicated terms in each of the following arithmetic progression:

a = 3, d = 2; ; t_{n}, t_{10}

Find the indicated terms in each of the following arithmetic progression:

a = 21, d = — 5; t_{n}, t_{25}

Find the indicated terms in each of the following arithmetic progression: