Question

(d) 1, 5, 9, 13, ...
4. For each sequence, find : (i) general rule (ii) nth term (ili) 100th term.​

Answer 1

$\huge{\pink{\underline{\underline{Answer:-}}}}$

Given:

Sequence 1,5,9,13

To find:

1. General rule = ?
2. nth term = ?
3. 100th term = ?

Explanation:

Formula for general term,

Formula for general 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

______________________________________

t100 = 1+ (100-1) 4

t100 = 1 + 99 × 4

t100 = 1+ 396

t100 = 397

Another method:

We find general rule tn = 4n - 3

So substituting n = 100

t100 = 4 × 100 - 3

t100 = 400 - 3

t100 = 397

Answer:

Therefore,

1. General rule = 4n - 3
2. nth term = 4n - 3
3. 100th term = 397

Verification of general rule:

General rule of the given sequence 1,5,9,13 is 4n-3

When n = 1

First term = 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

Basic point:

• Try solving more such questions to get good hold on it