Arithmetic sequence is given by a5 = 0 and a15 = 4.What is the sum of the first 15 terms of that arithmetic sequence? About the author Emma
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, [tex]\boxed{\tt S_n = \dfrac{n}{2}[2a+(n-1)d]}[/tex] 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 Reply
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 Reply
Answer:
The required sum of first 15 terms of the arithmetic sequence is 18
Step-by-step explanation:
Given :
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,
[tex]\boxed{\tt S_n = \dfrac{n}{2}[2a+(n-1)d]}[/tex]
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
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