Question

If the sum of first 4 terms of an AP is 40 and that of first 14 terms is 280, find the sum of its first n terms.
OR
Find the sum of the first 30 positive integers divisible by 6.

Answer 1

it's is correct answer

Answer 2

Answer:

n(n+6)

2790

Step-by-step explanation:

If the sum of first 4 terms of an AP is 40 and that of first 14 terms is 280, find the sum of its first n terms.

OR

Find the sum of the first 30 positive integers divisible by 6.

Let say first four terms of an AP are

a-3d , a-d , a+d , a + 3d

Sum pf 4 terms are

4a = 40

a = 10

so AP is

10-3d , 10-d , 10+d , 10+3d , 10+5d ......

a = 10-3d

cd = 2d

Sum of first 14 terms

=(n/2) (first + Last term)

= (14/2)(10 -3d  + 10-3d + 13*2d)

= 7 ( 20 + 20d)

Sum of first 14 terms = 280

7 ( 20 + 20d) = 280

=> 20 + 20d = 40

=> 20d = 20

=> d = 1

AP is

7 , 9 , 11 , 13 , 15

first term  = 7

cd = 2

Sum of first n terms

= (n/2)(a + a +(n-1)cd)

=(n/2)(7 + 7 + (n-1)2)

= (n)(7 + n-1)

= n (n+6)

first 30 positive integers divisible by 6

6 , 12 , 18....................................174 , 180

a = 6

d = 6

n = 30

Sum = (30/2) (6 + 6 + 29(6))

= 15 * 186

= 2790