Question

Find the fifteenth term of A.P. root2, root8, root18, .​

Answer 1

Answer: 16√2

Step-by-step explanation:

Given sequence is √2 , √8, √18,...

a1 = √2 ,

a2 = √8 = √ ( 2 × 2 ) ×2 = 2√2

a3 = √18 = √ ( 3 × 3 ) × 2 = 3 √2

First term (a ) = a1 = √2

a2 - a1 = 2√2 - √2 = √2

a3 - a2 = 3√2 - 2√2 = √2

Therefore ,

a2 - a1 = a3 - a2 = √2

Common difference (d) = √2

The given sequence is in A.P .

nth term = an = a + ( n-1 ) d

15th term of the A.P = a15

a15 = a + ( 15 - 1 ) d

= a + 14d

= √2 + 14 × √2

= √2 + 14√2

= 16√2

Answer 2

Answer:-

Given:

√2 , √8 , √18... are in AP.

a = √2

d = a(n) - a(n - 1)

→ d = a(2) - a

→ d = √8 - √2

→ d = √(4 * 2 ) - √2

→ d = 2√2 - √2

→ d = √2

We know that,

nth term of an AP [ a(n) ] = a + (n - 1)d

→ a (15) = √2 + (15 - 1) * (√2)

→ a(15) = √2 + 14 * √2

→ a(15) = √2 + 14√2

→ a(15) = 15√2

→ a(15) = √(2 * 15²)

→ a(15) = √450

Hence, the 15th term of the given AP is √450.

Additional Information:

• A series in which each term (except first term) differs from its preceding term by a fixed quantity is called an Arithmetic Progression (AP).

• The fixed quantity is called common difference.

• General form of an AP is a , a + d .... if a is the first term and d is the common difference.

• nth term of an AP is a + (n - 1)d.

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