Arithmetic questions

Question

what is the answer to if the 60th term of an arithmetic sequence is 110, and the common differnce is 8, what is the first term of the sequence?

Answer 1

To solve this question, we must utilize the arithmetic sequence formula. The arithmetic sequence formula is defined as a_n = (a_1)+ (n-1)d

a_n = nth term

a_1 = first term

n = term position

d=common difference

Plugging the given values you provided in that sequence, we get 110 = a_1 +(60-1)8. From there we need to solve for a_1.

1st step: is applying PEMDAS (Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction). Let us start with the right-hand side of the equation. Applying PEMDAS, we first solve by focusing on the parenthesis. In this case (60-1) is 59.

2nd step: Next in PEMDAS would be multiplication. We multiply in our equation of 110 = a_1 + (59)*8, 59 times 8 = 472. We are now left with 110=a_1+472.

3rd step: To isolate a_1, we must now subtract 472 on both sides to cancel out the 472 on the right-hand side. 110-472 = a_1 + (472 - 472). This now leads us to the answer of -362 = a_1 for which the numerical value -362 is the first term of the sequence.

Solution: -362