Question

Find the first four terms of the sequence given ai 31 and an+1 an 3.

Answer 1

Answer:

he arithmetic sequence ai is defined by the formula: a1= 2 ai= ai - 1 -3 find the sum of the first 335 terms in the sequence

Step-by-step explanation:

In an arithmetic sequence,

a_1=2a

1

=2

a_i=a_{i-1}-3a

i

=a

i−1

−3

To find:

The sum of the first 335 terms in the given sequence.

Solution:

The recursive formula of an arithmetic sequence is:

a_i=a_{i-1}+da

i

=a

i−1

+d ...(i)

Where, d is the common difference.

We have,

a_i=a_{i-1}-3a

i

=a

i−1

−3 ...(ii)

On comparing (i) and (ii), we get

d=-3d=−3

The sum of first i terms of an arithmetic sequence is:

S_i=\dfrac{i}{2}[2a+(i-1)d]S

i

=

2

i

[2a+(i−1)d]

Putting i=335,a=2,d=-3i=335,a=2,d=−3 , we get

S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)]S

335

=

2

335

[2(2)+(335−1)(−3)]

S_{335}=\dfrac{335}{2}[4+(334)(-3)]S

335

=

2

335

[4+(334)(−3)]

S_{335}=\dfrac{335}{2}[4-1002]S

335

=

2

335

[4−1002]

S_{335}=\dfrac{335}{2}(-998)S

335

=

2

335

(−998)

On further simplification, we get

S_{335}=335\times (-499)S

335

=335×(−499)

S_{335}=-167165S

335

=−167165

Therefore, the sum of the first 335 terms in the given sequence is -167165.