Question

Find the sum of the given arithmetic sequences.

2. 3,6,9, ... find 518.
​

Answer 1

Explanation:

Given S

16

=112

sum of next 14 terms = 518

S

n

=

2

n

[2a+(n−1)d]

S

16

=

2

16

[2a+(16−1)d]

112=8[2a+15d]

14=2a+15d⋯(1)

sum of next 14 terms is 518

sum of (16 + 14) terms (S

30

)=112+518

S

30

=630

S

30

=

2

30

[2a+(30−1)d]

630=15[2a+29d]

42=2a+29d⋯(2)

Subtracting equation (1) from (2)

42=2a+29d

14=2a+15d

- - -

_____________

28=14d.

d=28/14

d=2.

Substitute value of d in equation (1)

14=2a+15d

14=2a+15(2)

14=2a+30

2a=−16

a=−16/2

a=−8

If 'a' is the first term and 'd' is a common difference then the A.P is

a,a+d,a+2d,a+3d⋯

−8,−6,−4,−2⋯