Question

The fifth term of an AP is -15, second term is 0 find the

(a) first term
(b) common difference​

Answer 1

a) The first term of an AP can be found using the formula for the nth term of an AP, which is a + (n-1)d, where a is the first term, d is the common difference, and n is the position of the term.

Using this formula, we can substitute the known values: -15 = a + (5-1)d

-15 = a + 4d

To find the first term, we will have to solve for a by isolating it on one side of the equation:

a = -15 - 4d

b) To find the common difference, we can use the relation between the second and fifth term.

The fifth term of an AP is -15, and the second term is 0, so we can use the formula for the nth term of an AP to find the common difference:

-15 = a + (5-1)d

-15 = a + 4d

To find the common difference, we will have to solve for d by isolating it on one side of the equation:

d = (-15 - a) / 4

Answer 2

The first term of the arithmetic progression is 5, and the common difference is -5.

Step-by-step explanation:

In an arithmetic progression (AP), the nth term can be found using the formula a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference. Given that the fifth term (a_5) is -15 and the second term (a_2) is 0, we can set up two equations:

1) For a_5: -15 = a_1 + (5 - 1)d

2) For a_2: 0 = a_1 + (2 - 1)d

From equation 2, we find that a_1 = -d. Substituting a_1 into equation 1, we get: -15 = -d + 4d, which simplifies to 3d = -15. This gives us d = -5. Then, substituting d into a_1 = -d, we get a_1 = 5.

Therefore, the first term (a) is 5, and the common difference (b) is -5.