Find the 100th and the nth term for each of the following sequences.
a. The 100th term of 1, 3, 5, 7 is ?
The nth term of 1, 3, 5, 7 is ?
b. The 100th term of 60, 110, 160 is ?
The nth term of 60, 110, 160 is ?
c. The 100th term of 1,2,4 ... is ?
The nth term of 1, 2, 4 is ?
d. The 100th term if 8, 8^3 , 8^7 is ?
The nth term of 8, 8^3 , 8^7 is ?
e. The 100th term of 193 + 6 • 3^25 , 193 + 6 • 3^25 , 193 + 8 • 3^25 is ?
The nth term of 193 + 6 • 3^25 , 193 + 8 • 3^25 is ?
Answers
Answer:
Step-by-step explanation:
The 100th term of:-
a. 1, 3, 5, 7..... is 199.
b. 60, 110, 160,..... is 5010.
c. 1, 2, 4,.... is 2⁹⁹.
d. 8, 8^3, 8^7,... is neither A.P nor G.P
e. 193 + 6 • 3^25 , 193 + 6 • 3^25 , 193 + 8 • 3^25,.... is neither A.P nor G.P
The nth term of:-
a. 1, 3, 5, 7..... is 1 + (n - 1)2.
b. 60, 110, 160,..... is 60 + (n - 1)50.
c. 1, 2, 4,.... is 1x2ⁿ⁻¹.
d. 8, 8^3, 8^7,... is neither A.P nor G.P
e. 193 + 6 • 3^25 , 193 + 6 • 3^25 , 193 + 8 • 3^25,.... is neither A.P nor G.P
Given,
a., b., c., d., e. series.
To Find,
The 100th term and the nth term of a., b., c., d., e. series.
Solution,
a. In 1, 3, 5, 7.. series
first term (a) = 1
common difference (d) = 2
∴ 100th term = a + (100 - 1)d
= 1 + 99x2
= 199
∴ nth term = a + (n - 1)d
= 1 + (n - 1)2
b. In 60, 110, 160.. series
first term (a) = 60
common difference (d) = 50
∴ 100th term = a + (100 - 1)d
= 60 + 99x50
= 5010
∴ nth term = a + (n - 1)d
= 60 + (n - 1)50
c. In 1, 2, 4.. series
first term (a) = 1
common ratio (r) = 2
∴ 100th term = arⁿ⁻¹
= 1x2¹⁰⁰⁻¹
= 2⁹⁹
∴ nth term = arⁿ⁻¹
= 1x2ⁿ⁻¹
d. The given series is neither A.P nor G.P
e. The given series is neither A.P nor G.P
Hence, the 100th term and the nth term of the respective series are mentioned above.
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