Question

If the first term of an Ap is -11 and the fifth term is 1. What is the sum of the first eight terms?

Answer 1

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.