Question

which of the following are ap if they form the ap find the common difference d and write three more terms √2,√8√18√32​

Answer 1

➤ What is A.P ?

• A sequence is said to be an A.P if the difference of two consecutive terms is always same and this difference is called Common difference denoted by ' d ' and the first term of sequence is denoted by 'a'

★ Given:-

• a = √2

If it's form an Ap then it will have common difference.

Common Difference :-

• $\sf{a_2 - a_1}$

→ √8 - √2 

→ 2√2 - √2

→ √2

Similarly,.

• $\sf{a_3 - a_2}$

→ √18 - √8

→ 3√2 - 2√2

→ √2

• $\sf{a_4 - a_3}$

→ √32 - √18

→ 4√2 - 3√2

→ √2

Hence, Yep ! It's an ap as it's having common difference → √2.

Next three terms will be :-

→ Previous term + d

→ √32  + √2 

→ 4√2  + √2 

→ 5√2

→ √50

→ Previous term + d

→ √50 + √2

→ 5√2 + √2

→ 6√2

→ √72

→ Previous term + d

→ √72 + √2

→ 6√2 + √2

→ 7√2

→ √98

Next three terms area √50 , √72 and √98 respectively.

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