Given the Arithmetic sequence A1,A2,A3,A4 37, 46, 55, 64 What is the value of A36?

Answer 1

From what I can tell, it sounds like a₁ = 37, a₂ = 46, a₃ = 55, a₄ = 64. Find a₃₆. Is that right? If so, here is how I would go about solving the problem.

Since each value term is adding 9 to get your next term in the sequence (I.e. 37 + 9 = 46; 46 + 9 = 55; etc) we say that your common difference d = 9. Now think about how you would arrive at all of your terms:

a₂ = 37 + 9 = 46

a₃ = 37 + 2(9) = 55

a₄ = 37 + 3(9) = 64

see the pattern?

a_n = 37 + (n-1)9

So, a₃₆ = 37 + 36(9) = 361

In general, for any arithmetic sequence, the formula

a_n = a₁ + (n - 1)(d) tells you your n^th term of the sequence where a₁ is your first term, n is the term, and d is the common difference (I.e. how much you need to add/subtract in order to get to your next term).

Hope this helps.

Mr. K

Answer 2

d = 5

37 = a₁ + 4(5)

17 = a₁

a₃₆ = 17 + (35)(5)