Question

Determine the sum of the first 8 terms of the arithmetic sequence whose first 4 terms are 8, 11, 14, 17.

a) 76
b) 80
c) 82
d) 86

Answer 1

The sum of the first 8 terms of the arithmetic sequence is 148 after determining the common difference to be 3 and applying the formula for the sum of an arithmetic sequence. This result is not reflected in the options given, which suggests there may be an error in the question or options.

Step-by-step explanation:

To determine the sum of the first 8 terms of the arithmetic sequence whose first 4 terms are 8, 11, 14, and 17; we first need to find the common difference (d), then apply the formula for the sum of n terms of an arithmetic sequence (Sn = n/2(2a + (n-1)d)).

Step-by-step:

1. Determine the common difference (d):
   d = 11 - 8 = 3
2. Identify the first term (a) of the sequence:
   a = 8
3. Use the formula for the sum of an arithmetic sequence:
   S8 = 8/2[2(8) + (8-1)(3)]
4. Calculate the sum:
   S8 = 4[16 + 21]
   S8 = 4[37]
   S8 = 148

The sum of the first 8 terms of the sequence is 148, which is not among the options provided, indicating a potential error in the question or the provided options.