A calculated series is known as the 3rd term = 9, while the number of terms is 5 and 7 = 36, so the first 10 terms are
Answers
A calculated series is known as the 3rd term = 9, while the number of terms is 5 and 7 = 36, so the first 10 terms are 165.
DISCUSSION :
Arithmetic and Arithmetic Series
Arithmetic sequence is a sequence of numbers with each consecutive tribe having a fixed difference. The fixed difference is called difference.
a, a + b, a + 2b, a + 3b, ....
Different = b = U2 - U1
In general, the nth term arithmetic sequence is expressed by :
Un = a + (n - 1) b
While the Arithmetic Series is the sum of the arithmetic sequence terms. In general the number n of the first term arithmetic sequence is stated by :
Sn = U1 + U2 + U3 + ... Un
To calculate the sum used the formula:
Sn = n / 2 (2a + (n - 1) b) or
Sn = n / 2 (a + Un)
↓↓↓↓↓↓
Known:
U3 = 9
U5 + U7 = 36
Asked: The first 10 tribes?
Answer:
9 = U3
9 = a + (3 -1) b
9 = a + 2b ................ (1)
36 = U5 + U7
36 = (a + (5 - 1) b) + (a + (7 - 1) b)
36 = a + 4b + a + 6b
36 = 2a + 10b
36 = 2 (a + 5b)
18 = a + 5b ................. (2)
Elimination of equations (1) and (2)
a + 2b = 9
a + 5b = 18
____________-
3b = 9
b = 9/3
b = 3
Enter b = 3 in one equation (here we use equation 1)
9 = a + 2b
9 = a + 2.3
9 = a + 6
a = 9 - 6
a = 3
Then the first 10 terms are:
Sn = n / 2 (a + Un)
S10 = 10/2 (a + (a + 9b))
S10 = 5 (2a + 9b)
S10 = 5 (2 (3) + 9 (3))
S10 = 5 (6 + 27)
S10 = 5 × 33
S10 = 165
Step-by-step explanation:
9 = U3
9 = a + (3 -1) b
9 = a + 2b ................ (1)
36 = U5 + U7
36 = (a + (5 - 1) b) + (a + (7 - 1) b)
36 = a + 4b + a + 6b
36 = 2a + 10b
36 = 2 (a + 5b)
18 = a + 5b ................. (2)
using equations (1) and (2)
a + 2b = 9
a + 5b = 18
3b = 9
b = 9/3
b = 3
Substitute b = 3 in one equation
9 = a + 2b
9 = a + 2.3
9 = a + 6
a = 9 - 6
a = 3
Thus, the first 10 terms are:
Sn = n / 2 (a + Un)
S10 = 10/2 (a + (a + 9b))
S10 = 5 (2a + 9b)
S10 = 5 (2 (3) + 9 (3))
S10 = 5 (6 + 27)
S10 = 5 × 33
S10 = 165