Question

Is 203 any term of AP 1,7,13,19....?

Answer 1

Answer:

203 is not a term of the given A.P.

Step-by-step explanation:

Given:

• A.P is 1, 7, 13, 19......

To Find:

• If 203 is a term of the A.P

Solution:

Let us assume that 203 is a term of the A.P

Now we have to find which term of the A.P is 203.

The nth term of an A.P is given by,

aₙ = a₁ + (n - 1) × d

where aₙ is the nth term, a₁ is the first term, n is the number of term and d is the common difference.

The first term of the given A.P is 1

Common difference = a₂ - a₁ = 7 - 1 = 6

aₙ = 203

Substitute the data,

203 = 1 + (n - 1) × 6

203 = 1 + 6n - 6

203 = 6n - 5

203 + 5 = 6n

208 = 6n

n = 208/6

n = 34.67

Here n is not a positive whole number.

Hence 203 is not a term of the given A.P.

Notes:

The nth term of an A.P is given by,

aₙ = a₁ + (n - 1) × d

The common difference of an A.P is the difference between its two consecutive terms.

d = a₂ - a₁

$\tt{d=\dfrac{a_m-a_n}{m-n} }$