Question

What is the arithmetic sequence if 11th term is 58 and 31st term is 158?

Answer 1

Given :-

The 11th term of an arithmetic sequence is 58 .

31st term of an arithmetic sequence is 158 .

Required to find : -

• Arithmetic progession ?

SOLUTION  : -

11th term = 58

31st term = 158

We need to find the arithmetic progession ?

So,

We know that ;

The 11th term of an arithmetic sequence can be represented as " a + 10d "

The 31st term of an arithmetic sequence can be represented as " a + 30d "

This implies;

a + 10d = 58 ➡️ Equation - 1

Consider this as Equation - 1

a + 30d = 150 ➡️ Equation - 2

Consider this as Equation - 2

Now,

We need to solve these 2 equations simultaneously .

Let's use Elimination method . So, that by eliminating one variable we can simplify our calculations.

Subtract Equation 1 from the Equation 2

a + 30d = 158

a + 10d = 58

( − ) ( − ) ( − )

+20d = 100

➡️ 20d = 100

➡️ d = 100/20

➡️ d = 5

Substitute the value of d in Equation 1

=> a + 10d = 58

=> a + 10(5) = 58

=> a + 50 = 58

=> a = 58 - 50

=> a = 8

Hence,

• Common difference ( d ) = 5

• First term ( a ) = 8

Now,

Let's form the AP ;

➡️ 1st term = a = [ 8 ]

➡️ 2nd term = a + d = 8 + 5 = [ 13 ]

➡️ 3rd term = a + 2d = 8 + 2(5) = 8 + 10

➡️ 4th term = a + 3d = a + 3(5) = 8 + 15

AP = 8 , 13 , 18 , 23 . . . . . . . . . . . .

Required AP !

AP = 8 , 13 , 18 , 23 , . . . . . . . .

Additional Information

Question

What is an Arithmetic progession ?

Answer

An arithmetic progession is a sequence of terms whose common difference is constant/equal .