Use the formula for the sum of the first n terms of the arithmetic sequence to find the sum.

Question

Use the formula for the sum of the first n terms of the arithmetic sequence to find the sum.
16 + 25 + 34 + + 97
S10 =

Answer 1

You're told to use the formula for sum of n terms of an arithmetic sequence.

 

Read the formula from your textbook. Identify all the values of the particular parts, in your specific problem:

a₁ = 16

d = 9

n = 10 because nine additions of d=9 advances from first term 16 to 97, i.e. 97-16=81 = 9(9) so you have TEN terms.

 

Now plug into the formula to COMPUTE the sum.

Answer 2

a1=16,

a2=25,

a3=34,...

 

a2=a1+q (from here follows that q=9)

 

a3=a2+1=a1+2q,...,an=a1+(n-1)q.

 

 

Sn=a1+a2+...+an=a1+(a1+q)+(a1+2q)+...+(a1+(n-1)q)=

 

=n*a1+[q+2q+...+(n-1)q]=

 

=n*a1+q*(1+2+...+(n-1))=

 

=n*a1+q*n*(n-1)/2= n(a1+q*(n-1)/2).

 

Noq S10=10(16+9*9/2)=5*(32+81)=5*113= 565.

 

 

[(a1+an)*n]/2=[(a1+a1+(n-1)q)*n]/2=[(2a1+(n-1)q)n]/2

 

for n=10 you can find

 

S10=[(2*16+9*9)*10]/2=(32+81)*5=113*5=