Question

find the sum of the first 20 terms whose 4th term is 18 and difference of 9th term from 15th term is 30​

Answer 1

Step-by-step explanation:

ATQ,

a4 = 18 => a + 17d = 18 (1)

and a15 - a9 = 30

=> a + 14d - ( a + 8d ) = 30

=> a + 14d - a - 8d = 30

=> 6d = 30

=> d = 30/6 = 5

So in (1)

=> a + 17 (5) = 18

=> a = 18 - 85

=> a = -67

Formula of sum -

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

S20 = 20/2 [ 2 × (-67) + (20-1)5 ]

= 10 ( -134 + 95 )

= 10 × (-39)

= -390