Question

Find Sn for the following arithmetic sequences described.

a1 = 132, d = -4, an = 52

Answer 1

We can use the formula for the nth term of an arithmetic sequence to find n:

an = a1 + (n - 1)d

Substituting the given values, we get:

52 = 132 + (n - 1)(-4)

Simplifying and solving for n, we get:

n = 21

So, the sequence has 21 terms.

We can use the formula for the sum of the first n terms of an arithmetic sequence to find Sn:

Sn = n/2(2a1 + (n - 1)d)

Substituting the given values, we get:

Sn = 21/2(2(132) + (21 - 1)(-4))

Simplifying, we get:

Sn = 21/2(264 - 80)

Sn = 21/2(184)

Sn = 1932

Therefore, the sum of the first 21 terms of the arithmetic sequence is 1932.