Question Video: Finding the General Formula of a Sequence Mathematics • Second Year of Secondary School

Video Transcript

Which of the following is an expression for the general term of the sequence 52, 84, 116, 148? Is it (A) 52 plus 30 multiplied by 𝑛 minus one? (B) 52 plus 32 multiplied by 𝑛 minus one. (C) 52 plus 32 multiplied by 𝑛 plus one. (D) 84 plus 32 multiplied by 𝑛 minus one. Or (E) 84 plus 30 multiplied by 𝑛 plus one.

We are told in the question that the first four terms of our sequence are 52, 84, 116, and 148. These correspond to the integer values of 𝑛, one, two, three, and four. In order to work out which of the expressions corresponds to this sequence, we can substitute these values into each expression in turn. Let’s begin with 𝑛 equals one. In option (A), we have 52 plus 30 multiplied by one minus one. As one minus one equals zero, this is equal to 52. This means that expression (A) does satisfy the first term of our sequence. This is also true of option (B). 52 plus 32 multiplied by one minus one is equal to 52. Options (C), (D), and (E) give values of 116, 84, and 144 when we substitute 𝑛 equals one. This means that these expressions do not have a first term equal to 52. And we can therefore rule out these options.

We will now substitute 𝑛 equals two into the expressions (A) and (B). In option (A), we have 52 plus 30 multiplied by two minus one, which is equal to 82. In option (B), we obtain the answer 84. Since the second term of our sequence is 84, we can rule out option (A). Whilst it appears that option (B) is the correct answer, it is worth checking that this is the correct expression for 𝑛 equals three and 𝑛 equals four. When 𝑛 is equal to three, the expression 52 plus 32 multiplied by 𝑛 minus one gives us 116. And when 𝑛 is equal to four, the expression gives us 148. These do correspond to the four terms of our sequence, and the correct answer is therefore option (B).