1) To find the common difference, we can use the formula for the nth term of an arithmetic progression:
nth term = a + (n-1)d
where "a" is the first term, "n" is the number of the term we want to find, and "d" is the common difference.
We are given that the fourth term is -3 and the ninth term is 12. Plugging these values into the formula, we get:
-3 = a + (4-1)d
12 = a + (9-1)d
Simplifying these equations, we have:
-3 = a + 3d
12 = a + 8d
Next, we can subtract the first equation from the second equation:
12 - (-3) = (a + 8d) - (a + 3d)
Simplifying this, we get:
15 = 5d
Dividing both sides by 5, we find:
d = 3
Therefore, the common difference is 3.
2) To find the fifth term, we can use the formula we derived earlier:
nth term = a + (n-1)d
Plugging in the values we know, we have:
fifth term = a + (5-1)d
Substituting the value of the common difference, we get:
fifth term = a + (4)(3)
Simplifying this equation, we find:
fifth term = a + 12
Since we don't have the information to determine the value of "a," we can't find the exact value of the fifth term.
3) To find the number of the term that will give a sum of 135, we can use the formula for the sum of the first n terms of an arithmetic progression:
Sum = (n/2)(2a + (n-1)d)
Plugging in the values we know and the given sum, we have:
135 = (n/2)(2a + (n-1)d)
Again, since we don't have the information to determine the value of "a," we can't find the exact number of the term that will give a sum of 135.
The fourth and ninth terms of an arithmetic progression are -3 and 12 respectively. Find the:
1) common difference
2) fifth term
3) number of term which will give a sum of 135
1 answer