Question

the 5th term of a linear sequence is 17 and the 6th term is 21 workout the 100th term?

Answer 1

Given:

5th term = a + 4d = 17

6th term = a + 5d = 21

To Find:

100th term

Solution:

a + 4d = 17 ....(1)

a + 6d = 21 ....(2)

Subtracting both Equation, we get

d = 2

Putting the value of d in equation (1)

a + 4(2) = 17

a + 8 = 17

a = 17 - 8

a = 9

Now, we have

a = 9

d = 2

We know that,

100th term = a + 99d

= 9 + 99(2)

= 9 + 198

= 207

Hence, the 100th term of a linear sequence is 207.

Answer 2

${\huge{\green{\underline{\green{\boxed{\sf { \red{Solution :}}}}}}}}$

a + 4d = 17 ....(1)

a + 6d = 21 ....(2)

Subtracting both Equation, we get

d = 2

Putting the value of d in equation (1)

$\implies$49x + 4(2) = 17

$\implies$a + 8 = 17

$\implies$a = 17 - 8

$\implies$a = 9

Now, we have

$\implies$a = 9

$\implies$d = 2

We know that,

100th term = a + 99d

$\implies$ 9 + 99(2)

$\implies$ 9 + 198

$\implies$ 207

The 100th term of a linear sequence is 207.