Question

Which of the following is a term of the sequence 3, 7, 11. . . .? (a) 184 (b) 185 (c) 186 (d) 187​

Answer 1

Step-by-step explanation:

Let a be the first term and d be the common difference.

First term a = 3.

Common difference d = 4.

Option Verification:

(1) 184.

= > an = a + (n - 1) * d

      184 = 3 + (n - 1) * 4

      184 = 3 + 4n - 4

      184 = 4n - 1

      185 = 4n

      n = 185/4.

N should be a positive integer, therefore 184 is not a term.

(2) 185

an = a + (n - 1) * d

185 = 3 + (n - 1) * 4

185 = 3 + 4n - 4

185 = 4n - 1

186 = 4n

n = 186/4

n should be a positive integer.. Therefore 186 is not a term.

(C) 186

= > an = a + (n - 1) * d

186 = 3 + (n - 1) * 4

186 = 3 + 4n - 4

186 = 4n - 1

187 = 4n

n = 187/4

n should be a positive integer.therefore 186 is not a term of the sequence.

(d) 187

= > an = a + (n - 1) * d

187 = 3 + (n - 1) * 4

187 = 3 + 4n - 4

187 = 4n - 1

188 = 4n

n = 188/4

n = 47.

Therefore 187 is a term of the sequence.

Hope this helps!