) How many terms of the following series are needed to make the given sum

Question

a) 5+8+11+14+...=670

 

b) 3+8+13+18+...=1575

 

c) 64+62+60+...=0

Answer 1

These are arithmetic sequences, so apply the sum formula: S_n = S₁ + (n - 1)d 

S_n: sum of the first n terms

 

S₁: the value of the first term

 

d: the difference between succeeding terms

 

a) S₁ = 5, d = +3.  You want to find n with S_n = 670.

 

5 + (n - 1)(3) = 670

 

3(n - 1) = 665

 

n = 222 2/3

 

You can interpret this as an impossible problem (assuming n is an integer) or round to 223 to reach 670.

 

 

 

b) S₁ = 3, d = 5, S_n = 1575

 

3 + 5(n - 1) = 1575

 

n = 315.4

 

 

n = 315 to reach 1575.

 

 

 

c) S₁ = 64, d = -1, S_n = 0

 

64 -2(n - 1) = 0

 

n = 33