Question

what is the 20th term of the sequence defined by an=4n-3?​

Answer 1

Answer:

a^10=4(20)-3

=80-3

=77

Answer 2

$\red\sf\boxed{20th \: term\: of \:the \:sequence = 77 }$

SOLUTION

Given that the Arithmetic Sequence is defined by  ,

an = 4n - 3

Here the value of n can be any natural numbers from 1 to infinity.

If n = 1 ,then

a × 1 = 4 × 1 -3

a = 4 - 3 = 1

If n = 2 , then

a2 = 4 × 2 - 3

a2 = 8 - 3 = 5

If n = 3 , then

a3 = 4 × 3 - 3

a3 = 12 - 3 = 9

So the Sequence is 1 , 5 , 9 , .......

Now let us find the common difference (d)

Common difference (d) = a2 - a1

                                       = 5 - 1  

                                       = 4

Now, we have the terms of AP and Common difference of the AP.

Next we have to find the  20th term of the AP

We know that an = a + (n-1)d

Here,

a = 1

d = 4

n = 20

$\implies$ a₂₀ = 1 + ( 20 -1 )4

$\implies$  a₂₀ = 1 + 19 × 4

$\implies$ a₂₀ = 1 + 76

$\implies$ a₂₀ = 77