Question

The second term of an arithmetic sequence is 7. The sum of the first 4 terms of the arithmetics sequence is 12. What is the first term a1, and the common difference, d, of the sequence?

Answer 1

To find the first term (a1) and common difference (d) of the arithmetic sequence, we can use the formulas: a1 = a2 - d and Sum of first n terms = (n/2)(2a1 + (n-1)d). Given the second term is 7 and the sum of the first 4 terms is 12, we can substitute these values into the formulas.

Step-by-step explanation:

To find the first term (a1) and common difference (d) of the arithmetic sequence, we can use the formulas:

a1 = a2 - d

Sum of first n terms = (n/2)(2a1 + (n-1)d)

Given that the second term (a2) is 7 and the sum of the first 4 terms is 12, we can substitute these values into the formulas.

Using the first formula, we have: a1 = 7 - d

Using the second formula, we have: 12 = (4/2)(2a1 + (4-1)d)

Simplifying the second equation, we get: 12 = 2(2a1 + 3d)

From here, we can solve for a1 and d using these two equations simultaneously.