Question

if in an AP the mean of Pth and qth term is equal to mean of earth and as the term then prove that P + Q is equal to R + s​

Answer 1

SOLUTION :

Let a be the first term and d be the common difference of the given AP. Then,

= ½ (T_p + T_q)= ½ (T_r + T_s)

= T_p + T_q = T_r + T_s

= [a + (p - 1)d]+ [a + (q - 1)d] = [a + (r - 1)d] + [a + (s - 1)d]

= 2a + (p + q - 2)d = 2a + (r + s - 2)d

= (p + q- 2)d = (r + s - 2)d

= P + q - 2 = r + s - 2

= p + q = r + s.

Hence, p + q = r + s.

Answer 2

Step-by-step explanation:

Given : -

• if in an AP the mean of Pth .

• qth term is equal to mean of earth

To prove : -

• then prove that P + Q is equal to R + s

Solution : -

A.M between p^th

term and q^ th

term = A.M between r^th

term and s^th

term of the A.P.

Let 'a' be first term of A.P and 'd' be common difference.

p^th term =a +( p - 1 )d

q^th term =a +( q - 1 )d

r^th term =a +( r - 1 )d

s^th term =a +( s - 1 )d

term =a+(s−1)d

( a + (p - 1) d + a + (q - 1 )d ) / 2 = a + (r - 1)d + a + (s - 1)d

2a +( p + q)d - 2d = 2a + (r + s )d - / 2d

p + q = r + s

more information : -

• A term is either a single number or variable, or the product of several numbers or variables.

• In elementary mathematics, a term is either a single number or variable, or the product of several numbers or variables.

For Example, : -

3x + 2x² + 5x + 1 = 2x² + (3+5)x + 1 = 2x² + 8x + 1, with like terms collected.

• A series is often represented as the sum of a sequence of terms.