Question

given an=4 d=2 sn= -14 find n and a​

Answer 1

Answer:

Step-by-step explanation:

Given that,

an = 4 and d = 2, Sn = - 14

an = a + ( n - 1 ) d

⇒ 4 = a + ( n - 1 ) ( 2 )

⇒ 4 = a + 2n - 2

⇒ 4 + 2 = a + 2n

⇒ a + 2n = 6------eq ( 1 ) ( say ).

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

⇒ - 14 = n / 2 [ a + ( n - 1 ) ( 2 ) ]

⇒ - 14 × 2 = n [ a + 2n - 2 ]

⇒ - 28 = n ( 6 - 2 ) (∵ a + 2n = 6 ----eq ( 1 ) )

⇒ - 28 = 4n

⇒ n = - 28 / 4

⇒ n = - 7

Now substituting " n = - 7 " in eq ( 1 ) , we get

a + 2 ( - 7 ) = 6

⇒ a - 14 = 6 ( ∵ + × - = - )

⇒ a = 6 + 14

⇒ a = 20.

∴ n = - 7 and a = 20 is the answer.