Question

The sum of First 9terms of an AP is 351 and the sum of its 20thterm is 1770.find the number

Answer 1

We know that the sum of 'n' numbers in AP
=>n/2[ 2a + (n - 1)d ]

where a = first Term of the series, n = no.of terms, d = Difference between terms

The sum of First 9terms of an AP is 351

=>9/2[ 2a + (9 - 1)d] = 351

=> 9[2a + 8d] = 351×2

=> 9[2a + 8d] = 702

=>(2a + 8d) = 702/9 = 78

=>2(a +4d) = 78

=>a + 4d = 78/2= 39

=>a + 4d = 39..(1)

=> a = 39 - 4d....(2)

The sum of its 20thterm is 1770

=>20/2[ 2a + (20 - 1)d ]= 1770

=>20[ 2a + 19d] = 1770×2

=> 40a + 380d = 3540

=>10(4a + 38d) = 10(354)

=>4a + 38d = 354

=> 2(2a + 19d) = 354

=> 2a + 19d = 354/2 = 177

=> 2a + 19d = 177 .....(3)

Now substitute (2) in (3)

2( 39 - 4d) + 19d = 177

78 - 8d +19d = 177

78 + 11d = 177

11d = 177 - 78

11d = 99

d = 99/11 = 9.

substitute 9 in (2)

a = 39 - 4(9)

a= 39 - 36 = 3.

a=3,d=9.