Terms,Arithmetic sequence

Question

The 16th term of an arithmetic sequence is 67 and the 301st term of the same sequence is 1207

(a) calculate the common difference and the first term

(b) simplify the formula for the general term

(c) Find the sun of the first 101 terms

Answer 1

Since there are 301-16 = 285 terms between the two given terms, we can calculate the common difference as such:

(1207 - 67)/285 = 4

To find the first term we follow a similar process. There are 15 terms between the 1st and 16th term, with a common difference of 4, so:

67 - 15(4) = 7

The general formula is : A_n = 7 + 4(n-1)

To find a sum, we use the formula S_n = (n(A₁ + A_n))/2 = 101(7 + 407)/2 = 20907