The 5th term of an ap is -3 its common difference is -4. What is the sum of its first 10 terms?
a + 4d = -3
You know d, so you can find a=13
S10 = 10/2 (2a + 9d) = 5(2*13 + 9*-4) = -50
or, since a+4d = -3 and d = -4, a+5d = -7
S10 = 10/2 (a+4d + a+5d) = 5(-3 + -7) = -50
vkbcfv
To find the sum of the first 10 terms of an arithmetic progression (AP), we need to know the first term, the common difference, and the number of terms. In this case, we are given the 5th term, the common difference, and we need to find the sum of the first 10 terms.
Let's use the formula for the nth term of an arithmetic progression:
Tn = a + (n - 1) * d,
where Tn is the nth term, a is the first term, n is the position of the term, and d is the common difference.
Given:
T5 = -3,
d = -4.
Substituting these values into the formula, we can solve for the first term (a):
T5 = a + (5 - 1) * (-4),
-3 = a + 4 * (-4),
-3 = a - 16.
Adding 16 to both sides:
-3 + 16 = a,
13 = a.
Now that we have the first term (a) and the common difference (d), we can use the formula for the sum of the first n terms of an arithmetic progression:
Sn = n/2 * (2a + (n - 1) * d),
where Sn is the sum of the first n terms.
Given:
n = 10,
a = 13,
d = -4.
Substituting these values into the formula, we can calculate the sum (Sn):
S10 = 10/2 * (2 * 13 + (10 - 1) * (-4)),
S10 = 5 * (26 - 36),
S10 = 5 * (-10),
S10 = -50.
Therefore, the sum of the first 10 terms of the arithmetic progression is -50.