what is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13?

Question

campbell_st · Answer

the general equation of a term in an arithmetic sequence is 

$$T_{n} = a + (n - 1)d$$
so setting up the equations you will have

$$8 = a + (6 -1) d$$

and 

$$13 = a + (10 -1) d$$


simplifying these equations you have 

$$8 = a + 5d$$

and 

$$13 = a + 9d$$

solve simultaneously using substitution

let a = 8 - 5d

then 13 = (8 - 5d) + 9d

or 13 = 8 + 4d

d = 1.25

substitute to find a

a = 1.75

now you have a, d and you know n = 4... 

so the general equation of the sum of an arithmetic sequence is 

$$S_{n} = \frac{n}{2}[2a + (n -1)d]$$

just substitute and solve.