Question

If the first term and common difference of an arithmetic sequence are equal, find the relation between 5th term and 10th term? ​

Answer 1

Answer:

10 th term =  twice of 5 th term

Step-by-step explanation:

first term a = common difference d

fifth term t5= a+(n-1)d

                  = a+ (5-1)d

                  =a+4d

                  =a+4a (because a =d)

                  =5a

tenth term t10= a+(n-1)d

                     =a+(10-1)d

                     =a+9d

                     =a+9a   (a=d)

                     =10a

therefore t5 = 2* t10

Answer 2

Given:

The first term = common difference.

To find:

To find the relation between the 5th term and 10th term of the sequence.

Solution:

The formula for finding the nth term in Arithmetic progression, A.P is,

A = a+ ( n-1 ) d

Where An = nth term of A.P.

A = first term

D = common difference

n = total number of terms

Since the first term is equal to the common difference,

Therefore,

a= d

a₅ = a + ( n-1) d

= a + ( 5- 1) d (n=5)

= a+ 4d ( a=d)

= a+4a

= 5a

A₁₀= a+ (n-1) d

= a + ( 10-1) d (n=10)

= a+ 9d

= a+ 9a

= 10a

A₅ = 5a                                   (equation 1)

A₁₀= 10a                                  (equation 2)

From equations 1 and 2,

A₁₀= 2 × a₅

The relation between 5th and 10th is that a₁₀ is twice the a₅ term.