Find the middle term of an ap 2,6,10,14 ,106
Answers
Answer:
an=106
a=2
d=4
an=a+ (n-1)d
106 = 2+(n-1)4
106= 2+4n-4
106=4n-2
108=4n
27=n
hence is odd so (n+1)/2
= (27+1)/2
= 14
14th term is the middle term
a14= a + (n-1)d
= 2+ (14-1)4
= 2+ 52
= 54
The middle term of the AP 2 , 6 , 10 , 14 , . . . , 106 is 54
Correct question : Find the middle term of an AP 2 , 6 , 10 , 14 , . . . , 106
Given :
The AP 2 , 6 , 10 , 14 , . . . , 106
To find :
The middle term of the AP 2 , 6 , 10 , 14 , . . . , 106
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 4 :
Write down the given progression
Here the given arithmetic progression is
2 , 6 , 10 , 14 , . . . , 106
Step 2 of 4 :
Write down first term and common difference
First term = a = 2
Common Difference = d = 6 - 2 = 4
Step 3 of 4 :
Calculate the number of terms in the AP
If possible let 106 is nth term of the AP
Then nth term of the AP = 106
a + (n - 1)d = 106
⇒ 2 + 4(n - 1) = 106
⇒ 2 + 4n - 4 = 106
⇒ 4n - 2 = 106
⇒ 4n = 108
⇒ n = 27
So there are 27 terms in the AP
Step 4 of 4 :
Calculate middle term of the AP
Number of terms in the AP = 27 which is odd
Hence middle term of the AP
━━━━━━━━━━━━━━━━
Learn more from Brainly :-
If for an A.P., S15= 147 and s14=123 find t 15
(A) 24 (B) 23 (C) 47 (D) 46
https://brainly.in/question/34324030
2. Insert there arithmetic means between -20 and 4
https://brainly.in/question/29887163
#SPJ3