Question

Arithmetic sequence is given by a5 = 0 and a15 = 4.
What is the sum of the first 15 terms of that arithmetic sequence?​

Answer 1

Answer:

The required sum of first 15 terms of the arithmetic sequence is 18

Step-by-step explanation:

Given :

• a₅ = 0
• a₁₅ = 4

To find :

the sum of first 15 terms of the arithmetic sequence

Solution :

nth term of an Arithmetic Sequence is given by,

aₙ = a + (n – 1)d

where

a denotes the first term

d denotes the common difference

5th term = 0

a + (5 – 1)d = 0

a + 4d = 0

a = –4d

15th term = 4

a + (15 – 1)d = 4

a + 14d = 4

Put a = –4d,

–4d + 14d = 4

10d = 4

d = 4/10

d = 0.4

Common differences = 0.4

first term, a = –4(0.4) = –1.6

Sum of first n terms of Arithmetic sequence is given by,

$\boxed{\tt S_n = \dfrac{n}{2}[2a+(n-1)d]}$

The sum of first 15 terms of the given Arithmetic sequence is

= 15/2 [2(-1.6) + (15–1)(0.4)]

= 7.5 [–3.2 + 14(0.4)]

= 7.5 [–3.2 + 5.6]

= 7.5 [2.4]

= 18

Therefore, the required sum of first 15 terms is 18

Answer 2

the required sum of first 15 terms is 18

Given :

a₅ = 0

a₁₅ = 4

To find :

the sum of first 15 terms of the arithmetic sequence

Solution :

nth term of an Arithmetic Sequence is given by,

aₙ = a + (n – 1)d

where

a denotes the first term

d denotes the common difference

5th term = 0

a + (5 – 1)d = 0

a + 4d = 0

a = –4d

15th term = 4

a + (15 – 1)d = 4

a + 14d = 4

Put a = –4d,

–4d + 14d = 4

10d = 4

d = 4/10

d = 0.4

Common differences = 0.4

first term, a = –4(0.4) = –1.6

The sum of first 15 terms of the given Arithmetic sequence is

= 15/2 [2(-1.6) + (15–1)(0.4)]

= 7.5 [–3.2 + 14(0.4)]

= 7.5 [–3.2 + 5.6]

= 7.5 [2.4]

= 18

Therefore, the required sum of first 15 terms is 18