D) Ifa, b and c are in A.P. than the relation between them is given by

1.	D) Ifa, b and c are in A.P. than the relation between them is given by (i) 2b = ato (ii) 2a =b+c (iii) a =b+c(iv) 2c = a+b
Answer» $\displaystyle\huge\red{\underline{\underline{Solution}}}$ CORRECT QUESTION Ifa, b and C are in A.P. than the relation between them is given by (i) 2b = a + c (ii) 2a =b+c (III) a =b+c (iv) 2C = a+b CALCULATION Let d be the Common DIFFERENCE of the Arithmetic progression Now first term = a So Second Term = a + d Third Term = a + 2d Again it is given that the three terms of the Arithmetic progression is a , b , c Therefore $\sf{b = a + d \: \: \: and \: \: \: c = a + 2d}$ Hence $\sf{2b}$ $= \sf{2(a + d)}$ $= \sf{2a + 2d}$ $= \sf{a + (a + 2d)}$ $= \sf{a + c}$ $\sf{Hence \: \: \: 2b = a + c}$ RESULT If a, b and c are in A.P. than the relation between them is given by (i) 2b = a + c ━━━━━━━━━━━━━━━━ LEARN MORE FROM BRAINLY Find the 100th term of an AP whose NTH term is 3n+1 brainly.in/question/22293445

D) Ifa, b and c are in A.P. than the relation between them is given by (i) 2b = ato (ii) 2a =b+c (iii) a =b+c(iv) 2c = a+b

Answer»

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

CORRECT QUESTION

Ifa, b and C are in A.P. than the relation between them is given by

(i) 2b = a + c

(ii) 2a =b+c

(III) a =b+c

(iv) 2C = a+b

CALCULATION

Let d be the Common DIFFERENCE of the Arithmetic progression

Now first term = a

Second Term = a + d

Third Term = a + 2d

Again it is given that the three terms of the Arithmetic progression is a , b , c

Therefore

$\sf{b = a + d \: \: \: and \: \: \: c = a + 2d}$

Hence

$\sf{2b}$

$= \sf{2(a + d)}$

$= \sf{2a + 2d}$

$= \sf{a + (a + 2d)}$

$= \sf{a + c}$

$\sf{Hence \: \: \: 2b = a + c}$

RESULT

If a, b and c are in A.P. than the relation between them is given by

(i) 2b = a + c

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

Find the 100th term of an AP

whose NTH term is 3n+1

brainly.in/question/22293445