SOLUTION: The sum of the first 12 terms of an AP (Arithmetic Progression) is 222, the sum of the first 5 terms is 40. Write out the first four terms of the series.
Question 142024: The sum of the first 12 terms of an AP (Arithmetic Progression) is 222, the sum of the first 5 terms is 40. Write out the first four terms of the series. Answer by nabla(475) (Show Source): You can put this solution on YOUR website! The sum of the first n terms of an arithmetic progression is .
Using this formula with n=12 and n=5,
simplifying a bit:
and simplifying a bit more:
We now solve this system of equations.
Solve: We'll use substitution. After moving 11*r to the right, we get: , or . Substitute that
into another equation: and simplify: So, we know that r=3. Since , a=2.
Answer: .
a=2, r=3.
The first 4 terms of the series would be, then:
2,(2+3),(2+2(3)),(2+3(3)) which is
2,5,8,11
In order to check, which is always a good idea, we can only iterate:
2+5+8+11+14=40 (first part is correct)
2+5+8+11+14+17+20+23+26+29+32+35=222 (second part is correct).