Question

Find the common difference of the arithmetic sequence with a⁴=10 and a¹¹ =45? what is the solution

Answer 1

Answer:

cd = 5

Step-by-step explanation:

nth term = a+(n-1)d

a4 = 10

a11 = 45

4th term = a+(4-1)d = a+(3)d = 10 ----(1)

11th term = a+(11-1)d = a+10d = 45 ---(2)

(2)-(1) = 7d = 35 = d =5

a = 10 -3(5) = 10-15 = 5

Answer 2

Answer:

The common difference 'd' is 5

Step-by-step explanation:

In arithmetic sequence general term is defined as $a_n = a+(n-1)d$

Given: $a_4 = 10$ and $a_1 = 45$

so,  

$a_4=a+(4-1)d$

$10=a+3d$   ......... (1)

and  

$a_1=a+(11-1)d$

$45=a+10d$   ......... (2)

Subtract equation (1) from equation(2)

$a_1 - a_4=(a+10d)-(a+3d)$

$45 - 10= a+10d- a-3d$

$35=7d$

dividing both the sides by 7,

$\frac{35}{7}=d$

$5=d$

Therefore, the common difference 'd' is 5