Question

Identify the arithmetic sequence(s).

• A. $4^2,5^2,6^2,7^2,8^2$
• B. $\sqrt{25},\sqrt{36},\sqrt{49},\sqrt{64},\sqrt{81}$
• C. $1^2+2^2,3^2+4^2,3^2+6^2,4^2+7^2$
• D. $25,31,37,43,49$

Answer 1

Answer: (B), (C), (D)

$25,31,37,43,49$

Let's check each option one by one.

$4^2,5^2,6^2,7^2,8^2$
$\Rightarrow 16,25,36,49,64$
In this sequence, the difference between any two consecutive terms is not the same
$25-16=9$
$36-25=11$
Hence, this pattern is not an arithmetic sequence.

$\sqrt{25},\sqrt{36},\sqrt{49},\sqrt{64},\sqrt{81}$
$\Rightarrow 5,6,7,8,9$
In this sequence, the difference between any two consecutive terms is $1.$
$6-5=1$
$7-6=1$
$8-7=1$
$9-8=1$
$\therefore$ It is an arithmetic sequence.

$1^2+2^2,3^2+4^2,3^2+6^2,4^2+7^2$
$\Rightarrow 1+4,9+16,9+36,16+49$
$\Rightarrow 5,25,45,65$
In this sequence, the difference between any two consecutive terms is $20.$

$25,31,37,43,49$
In this sequence, the difference between any two consecutive terms is $6.$
Hence, this is an arithmetic sequence.