Question

Please solve this fast .
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Answer 1

Given :

Sequence 1, 5 , 9 , 13

To find :

1 : General Rule = ?

2 : Nth term = ?

3 : 100th term = ?

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Explanation :

$formula \: for \: genral \: term \: tn \: = a \: + (n - 1) \: d \:$

a = First term

n = 1 , 2 , 3 , ....... term given

d = common difference between terms.

here, a = 1

d = 4 {5 -1 = 4, 9 -5 = 4, 13 - 9 = 4 }

tn = a + {n -1} d

tn = 1 + {n -1} 4

tn = 1 + 4n -4

tn = 4n - 3

nth term is 4n - 3

t 100 = 1 + (100-1) 4

t 100 = 1 + 99 × 4

t 100 = 1+ 396

t 100 = 397

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Verification of general rule :

General rule of the given sequence

1, 5 , 9 , 13 is 4n - 3

When n = 1

First terms = 4n -3 = 4×1 - 3 = 4-3 = 1

n = 2

Second term = 4n - 3 = 4 × 2 - 3 = 8-3 = 5

n = 3

Third term = 4n - 3 = 4×3 -3 = 12 -3 = 9

n = 4

Fourth term = 4n - 3 = 4 × 4 - 3 = 16 -3 = 13

Hence, proved the general rule is true.

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Hope it helps u.