Math, asked by Lesliemaddison24261, 10 months ago

Find the middle term of an ap 2,6,10,14 ,106

Answers

Answered by ankitchaudhary1997
8

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

Answered by pulakmath007
1

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

\displaystyle \sf{   =\bigg( \frac{27 + 1}{2} \bigg) }th \: term

\displaystyle \sf{   =\bigg( \frac{28}{2} \bigg) }th \: term

\displaystyle \sf{    = 14}th \: term

\displaystyle \sf{  = a_{14}  }

\displaystyle \sf{   = a + (14 - 1)d}

\displaystyle \sf{   = a + 13d}

\displaystyle \sf{   = 2 +( 13 \times 4)}

\displaystyle \sf{   = 2 +52}

\displaystyle \sf{  = 54 }

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. 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

Similar questions