If the first term of an Ap is -11 and the fifth term is 1. What is the sum of the first eight terms?
We can use the formula for the nth term of an arithmetic progression to solve this problem. The formula is:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
We know that a1 = -11 and a5 = 1. We can use these values to find the common difference:
a5 = a1 + (5-1)d
1 = -11 + 4d
d = 3
Now that we know the common difference, we can find the sum of the first eight terms using the formula:
Sn = n/2[2a1 + (n-1)d]
Substituting the values we know:
S8 = 8/2[2(-11) + (8-1)(3)]
S8 = 4[-22 + 21]
S8 = -4
Therefore, the sum of the first eight terms is -4.
To find the sum of the first eight terms of an arithmetic progression (AP), we need to find the common difference (d) between terms.
In an AP, the formula to find the nth term is given by:
Tn = a + (n-1)d
Given that the first term (a) is -11 and the fifth term (T5) is 1, we can substitute these values into the formula:
T5 = a + (5-1)d
1 = -11 + 4d
Solving this equation will give us the value of d:
4d = 12
d = 12/4
d = 3
Now that we know the common difference is 3, we can find the sum of the first eight terms (S8) using the formula:
S8 = (n/2)(2a + (n-1)d)
Substituting the values into the formula:
S8 = (8/2)(2(-11) + (8-1)(3))
S8 = 4(-22 + 7(3))
S8 = 4(-22 + 21)
S8 = 4(-1)
S8 = -4
Therefore, the sum of the first eight terms of the arithmetic progression is -4.