Find the first three terms of the arithmetic sequence in which n=39, a of n = 134.4, and S of n = 5538

Question

campbell_st · Answer

ok... so you are given 

n = 39

so for the 39th term you have

$$134.4 = a + 39 - 1) \times d.....or......  134.4 = a + 38d$$

now for the sum of 39 terms 

$$5538 = \frac{39}{2} \times [ 2a + (39 - 1) d] ... or.... 5538 = \frac{39}{2}[2a + 38d]$$

simplify the 2nd equation to 

11076 = 78a + 1482d

So I would use substitution 

take the 1st equation and make a the subject

a = 134.4 - 38d

and substitute it into the 2nd equation 

11076 = 38(134.4 - 38d) + 1482d

11076 = 5107.2 - 1444d + 1482d

solve for d.

when you get d, substitute it into either of the equations to find a, the 1st term. 

hope it helps

anonymous · Answer

Thank you so much, this really helps