Sequence questions final exam review questions that are giving me trouble.

Question

1. For the sequence 3,7,11,15, ... find:

 

a)The value of the 15th term

 

b)sum of the first 11 terms

 

 

 

 I know it's easy just to keep adding by 4 until 15 but can you do it through the formula way? because on the exam I'm expecting big numbers. Thanks

Answer 1

a_n = a₁ + (n - 1)d, where a_n = nth term, a₁ = first term, n = number of terms, d = common difference

 

a₁₅ = 3 + (15 - 1)4

a₁₅ = 3 + 14(4)

a₁₅ = 3 + 56 

a₁₅ = 59

 

S_n = (n/2)(2a₁ + (n - 1)d)

S₁₁ = (11/2)(2(3) + (11 - 1)4)

S₁₁ = (11/2)(6 + 40)

S₁₁ = (11/2)(46)

S₁₁ = 253

Answer 2

t(n)=t(1)+d(n-1)

t(15)=3+4(15-1)

t(15)=3+4(14)

t(15)=3+56

t(15)=59

 

S(n)=(n/2)(2a+d([n-1])

S(11)=(11/2)(2*3+4([11-1])

S(11)=(11/2)(6+4*10)

S(11)=(11/2)(46)

S(11)=11*23

S(11)=253