Question

find the sum of the two middle most terms of ap -4/3,-1,-2/3,41/3

Answer 1

Answer:

(i) The given progression 9, 15, 21, 27, ... .

Clearly, 15 − 9 = 21 − 15 = 27 − 21 = 6 (Constant)

Thus, each term differs from its preceding term by 6. So, the given progression is an AP.

First term = 9

Common difference = 6

Next term of the AP = 27 + 6 = 33

(ii) The given progression 11, 6, 1, −4, ... .

Clearly, 6 − 11 = 1 − 6 = −4 − 1 = −5 (Constant)

Thus, each term differs from its preceding term by −5. So, the given progression is an AP.

First term = 11

Common difference = −5

Next term of the AP = −4 + (−5) = −9

(iii) The given progression −1, -56, -23, -12, ...

Clearly, -56--1=-23--56=-12--23=16 (Constant)

Thus, each term differs from its preceding term by 16. So, the given progression is an AP.

First term = −1

Common difference = 16

Next term of the AP = -12+16=-26=-13

(iv) The given progression 2, 8, 18, 32, ...

This sequence can be re-written as 2, 22, 32, 42, ...

Clearly, 22-2=32-22=42-32=2 (Constant)

Thus, each term differs from its preceding term by 2. So, the given progression is an AP.

First term = 2

Common difference = 2

Next term of the AP = 42+2=52=50

(v) The given progression 20, 45, 80, 125, ...

This sequence can be re-written as 25, 35, 45, 55, ...

Clearly, 35-25=45-35=55-45=5 (Constant)

Thus, each term differs from its preceding term by 5. So, the given progression is an AP.

First term = 25=20

Common difference = 5

Next term of the AP = 55+5=65=180

Step-by-step explanation:

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