Given an arithmetic sequence with a2= 4and a6 =14 , find the following

Question

a) Find d

b) Find the first term of the sequence

c) Find a formula for the nth term of the sequence

d) Find the 25th term

e) Find the sum of the first 25 terms

Answer 1

Arithmetic sequence is given by

an = a1+ (n-1)d

a2=a1+(2-1)d

4= a1+d

a1+d=4 ———————1

a6=a1+(6-1)d

a1+5d=14———————2

Part a)

Using elimination method you can find d

subtract equation 2-equation 1

4d=10

d=10/4

d=2.5

Part b)

a1+d = 4

a1+ 2.5=4

a1= 4-2.5

a1= 1.5

Part c)

you can get the nth term of this sequence by substituting the values of a1 and d in the following general formula

an = a1+ (n-1)d

Part d)

substitute n= 25, a1=1.5, and d=2.5 in the above formula and you’ll be able to get the answer

Part e)

Sum of first n terms is given by:

n/2( 2a1 + (n-1)d )

if you plug in the values you’ll be able to get the answer.

Hope this helps!