T7=13,S14=203 then find S8
Answers
Answer:
44
Step-by-step explanation:
Given
T7 = 13, S14 = 203 then find S8
ANSWER
Given in an A.P T7 = 13
We know that nth term of an A.P is
T n = a + (n – 1) d
T 7 = a + (7 – 1) d
13 = a + 6d ------------(1)
Now S 14 = 203
We know that
Sum to n terms of an A.P is given by
S n = n/2 (2 a + (n – 1)d)
S 14 = 14/2 (2a + (14 – 1)d)
203 = 7(2a + 13d)
203/7 = 2a + 13d
2a + 13d = 29------------(2)
From 1 and 2 we get
a + 6d = 13
2a + 13d = 29
Multiplying equation 1 by 2 and subtracting we get
2a + 12d = 26
2a + 13d = 29
d = 3
Substituting in equation 1 we get
a + 6(3) = 13
a = 13 – 18
a = - 5
Now we need to find sum to n terms
Sn = n/2 (2a + (n – 1)d)
S8 = 8/2 (2(-5) + (8 – 1)3
S8 = 4(-10 + 21)
S8 = 44
Answer:
44
Step-by-step explanation:
Given
T7 = 13, S14 = 203 then find S8
ANSWER
Given in an A.P T7 = 13
We know that nth term of an A.P is
T n = a + (n – 1) d
T 7 = a + (7 – 1) d
13 = a + 6d ------------(1)
Now S 14 = 203
We know that
Sum to n terms of an A.P is given by
S n = n/2 (2 a + (n – 1)d)
S 14 = 14/2 (2a + (14 – 1)d)
203 = 7(2a + 13d)
203/7 = 2a + 13d
2a + 13d = 29------------(2)
From 1 and 2 we get
a + 6d = 13
2a + 13d = 29
Multiplying equation 1 by 2 and subtracting we get
2a + 12d = 26
2a + 13d = 29
d = 3
Substituting in equation 1 we get
a + 6(3) = 13
a = 13 – 18
a = - 5
Now we need to find sum to n terms
Sn = n/2 (2a + (n – 1)d)
S8 = 8/2 (2(-5) + (8 – 1)3
S8 = 4(-10 + 21)
S8 = 44
❤️THANKS AND MARK AS BRAINYLIST