Question Video: Using an Arithmetic Sequence to Solve a Problem in a Real Life Context Mathematics • Second Year of Secondary School

Video Transcript

A man works in a grocery store. He stacks tuna cans in rows, where there are 92 cans in the first row, 89 in the second, 86 in the third, and so on. Find the number of cans in the 12th row.

Well, first of all, what we can do is write this down as a sequence. So we’ve got 92, 89, and 86, because this is the number of cans of tuna in our rows. And what we can see is that we have a common difference or constant difference. And that is negative three, because we subtract three from the term to get the next term. So 92 minus three is 89. 89 minus three is 86.

And when we have a sequence that has a constant or common difference, then we can say that this is gonna be an arithmetic sequence. And for an arithmetic sequence, we in fact have a general form for the 𝑛 term. And that common form is that the 𝑛 term or 𝑎 sub 𝑛 is equal to 𝑎 sub one, which is our first term, plus 𝑛 minus one, where 𝑛 is our term number, multiplied by 𝑑, where 𝑑 is our common difference.

Well, in our sequence, we can see that 𝑎 sub one, our first term, is equal to 92. 𝑑, our common difference, is negative three. So therefore, if we want to find the number of cans in the 12th row — so this is gonna be our 12th term — then we can substitute these values into the general form I’ve shown.

So therefore, what we’re gonna get is 𝑎 sub 12 is equal to 92 plus 12 minus one multiplied by negative three. So this is gonna be 𝑎 sub 12 is equal to 92 plus 11 multiplied by negative three. Which gonna give us 𝑎 sub 12 is equal to 92 minus 33. So therefore, 𝑎 sub 12 is gonna be equal to 59. So we can say that the number of cans in the 12th row is 59 cans.