Question

The third term of an ARITHMETIC PROGRESSION is ten more than the first while the fifth term Is 15 more than the second term. Find the 15 term.

Answer 1

Check did you wrote the question correctly, because this can't be solved.

In AP n-th term is:

an = a ( n - 1 ) d

where

a = a1 = first term

d = common differrnce

In this case:

a2 = a + d

a3 = a + 2d

The third term of an AP is ten more than the first, means:

a3 = a + 10

a + 2 d = a + 10

Subtract a to both sides.

2 d = 10

d = 10 / 2

d = 5

a5 = a + 4 d

The fifth term Is 15 more than the second term, means:

a5 = a2 + 15

a + 4 d = a + d + 15

Again subtract a to both sides.

4 d = d + 15

Subtract d a to both sides.

3 d = 15

d = 15 / 3

d = 5

So we can find the common difference, but we can't find the first term.

Check did you wrote correctly.

Answer 2

a3-a = 2d = 10
so d = 5
Not enough information to find a