Question

23. If an = 5 - 7n , prove that (an )is an A.P.and sn​

Answer 1

Answer:

an = 5-7n

A1 = 5-7(1) = 5-7= -2

A2 = 5-7(2) = 5-14 = -9

A3 = 5-7(3)= 5-21 = -16

in an AP

a2- a1= a3- A2

-9-(-2) = -16-(-9)

-9+2= -16+9

-7 = = -7

LHS = RHS

SO IT IS IN AP

Sn = (n/2) ( 2a+(n-1) d)

Sn = n/2( 2x-2 + (n-1)X -7)

Sn = n/2( -4-7n+7)

Sn = n/2(3-7n)

Sn = (3n-7n²)/2