The sum of the first 4 termis of an arithmetic sequence is 24 . The term exceeds the term by
24. Determine the sum of the first 12 terms.
opyright Kevin Smith / Berlut Books CC

To find the sum of the first 12 terms of the arithmetic sequence, we start with the information given. Let the first term be and the common difference be . The sum of the first four terms can be expressed as:

From this, we simplify to:

Next, we know the 7th term exceeds the 3rd term by 24:

This simplifies to:

Substituting into equation (1):

Now we have and .

To find the sum of the first 12 terms , we use the sum formula for an arithmetic sequence:

Substituting :

Thus, the sum of the first 12 terms is .