Which of the following series is an arithmetic progression ? A) 2, 4,

1.	Which of the following series is an arithmetic progression ? A) 2, 4, 6, 8, B) 1, 2, 4, 8, C) 4, 9, 16, 25, D) 3, 9, 12, 18,
Answer» Correct option is A) 2, 4, 6, 8, (A) 2, 4, 6, 8, ...... \(a_2-a_1\) \(=4-2=2\) \(a_3-a_2\) \(=6-4=2\) and \(a_4-a_3\) \(=8-6=2\) \(\because\) \(a_4-a_3\) \(=a_3-a_2\) \(=a_2-a_1\) \(=2\) \(\therefore\) 2, 4, 6, 8, ...... is an arithmetic progression. (B) 1, 2, 4, 8, ........ \(a_2-a_1\) \(=2-1=1,\) \(a_3-a_2\) \(=4-2=2\) \(\because\) \(a_3-a_2\) \(\neq a_2-a_1\) \(\therefore\) 1, 2, 4, 8, ........ will not form an A.P. (C) 4, 9, 16, 25, ....... \(a_2-a_1\) \(=9-4=5,\) \(a_3-a_2\) \(=16-9=7\) \(\because\) \(a_3-a_2\) \(\neq a_2-a_1\) \(\therefore\) 4, 9, 16, 25, ....... will not form an A.P. (D) 3, 9, 12, 18, ......... \(a_2-a_1\) \(=9-3=6,\) \(a_3-a_2\) \(=12-9=3\) \(\because\) \(a_3-a_2\) \(\neq a_2-a_1\) \(\therefore\) 3, 9, 12, 18, ......... will not form an A.P. Correct option is A) 2, 4, 6, 8,

Which of the following series is an arithmetic progression ? A) 2, 4, 6, 8, B) 1, 2, 4, 8, C) 4, 9, 16, 25, D) 3, 9, 12, 18,

Answer»

Correct option is A) 2, 4, 6, 8,

(A) 2, 4, 6, 8, ......

\(a_2-a_1\) \(=4-2=2\)

\(a_3-a_2\) \(=6-4=2\)

and \(a_4-a_3\) \(=8-6=2\)

\(\because\) \(a_4-a_3\) \(=a_3-a_2\) \(=a_2-a_1\) \(=2\)

\(\therefore\) 2, 4, 6, 8, ...... is an arithmetic progression.

(B) 1, 2, 4, 8, ........

\(a_2-a_1\) \(=2-1=1,\)

\(a_3-a_2\) \(=4-2=2\)

\(\because\) \(a_3-a_2\) \(\neq a_2-a_1\)

\(\therefore\) 1, 2, 4, 8, ........ will not form an A.P.

(C) 4, 9, 16, 25, .......

\(a_2-a_1\) \(=9-4=5,\)

\(a_3-a_2\) \(=16-9=7\)

\(\because\) \(a_3-a_2\) \(\neq a_2-a_1\)

\(\therefore\) 4, 9, 16, 25, ....... will not form an A.P.

(D) 3, 9, 12, 18, .........

\(a_2-a_1\) \(=9-3=6,\)

\(a_3-a_2\) \(=12-9=3\)

\(\because\) \(a_3-a_2\) \(\neq a_2-a_1\)

\(\therefore\) 3, 9, 12, 18, ......... will not form an A.P.

Correct option is A) 2, 4, 6, 8,