find the 10th term from the end of A.p 3,8,13,18.....253
Answers
The 10th term from the end of AP 3 , 8 , 13 , 18 . . . . . , 253 is 208
Given :
The AP 3 , 8 , 13 , 18 . . . . . , 253
To find :
10th term from the end of the AP
Solution :
Concept :
If in an arithmetic progression
First term = a
Common difference = d
Then nth term of the AP
= a + ( n - 1 )d
Solution :
Step 1 of 3 :
Write down the given progression
Here the given arithmetic progression is 3 , 8 , 13 , 18 . . . . . , 253
We have to find the 10th term from the end of AP 3 , 8 , 13 , 18 . . . . . , 253
Which is exactly 10th term from first of the AP 253 , 248 , 243 , . . . , 8 , 3
Step 2 of 3 :
Write down first term and common difference
The arithmetic progression is
253 , 248 , 243 , . . . , 8 , 3
First term = a = 253
Common Difference = d = 248 - 253 = - 5
Step 3 of 3 :
Find the required 10th term
10th term of the AP
= a + ( n - 1 )d
= 253 + ( 10 - 1 ) × ( - 5 )
= 253 - 45
= 208
The 10th term from the end of AP 3 , 8 , 13 , 18 . . . . . , 253 is 208
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Given,
An Arithmetic Progression (A.P.): 3,8,13,18,-------253
To find,
The 10th term from the end of the A.P.
Solution,
We can simply solve this mathematical problem using the following process:
Mathematically,
For any A.P., its common difference can be calculated as the difference of the preceding term from the succeeding term.
{Statement-1}
For an A.P. with the first term a and common difference d, its n-th term can be represented as;
n-th term of the A.P.= An = a + (n-1)d
{Statement-2}
Now, according to the given A.P.;
The first term = 3
The common difference
= (second term) - (first term)
{according to statement-1}
= 8-3 = 5
Now, let us assume that the last term of the A.P. is the n-th term of the A.P.
=> The last term of the A.P. = An = 253
{according to statement-2}
=> a + (n-1)d = 253
=> 3 + (n-1)5 = 253
=> 5(n-1) = 253-3 = 250
=> (n-1) = 250/5 = 50
=> n-1 = 50
=> n = 50+1
=> n = 51
=> the given A.P. has a total of 51 terms
So,
The 10th term from the end of the A.P.
= the 42nd term of the given A.P.
= A(42)
= a + (42-1)d
{according to statement-2}
= 3 + (41×5)
= 3 + 205
= 208
Hence, the 10th term from the end of the A.P. is 208.