Question

In an AP , the first term is 22 ,nth term is - 11 and the sum of first n terms is 66. the value of n is with explanation​

Answer 1

a = 22

aₙ = -11

⇒ -11 = 22 + ( n - 1 ) d

( n - 1 ) d = -11 -22

( n - 1 ) d = -33 -----(i)

Also,

⇒ Sₙ = n/2 ( a + aₙ )   [ Here, aₙ is last term ]

66 = n/2 ( 22 + (-11) )

132 = n ( 11 )

n = 132 / 11

n = 12

Putting this value in ( i ) equation ;

( 12 - 1 ) d = -33

11d = -33

d = -3

Hope, it helps u.... :D