The sixth term of an ap is -10. 10th term is -26. Find 15th term of ap
The 10th term iks 4 terms after the 6th.
So, 4d = -26 - (-10) = -16
d = -4
Now the 15th term is 5 terms past the 10th term, so add 5d to -26.
10th grade "B"section so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so so help me
To find the 15th term of the arithmetic progression, we can first determine the common difference (d) between the terms.
Given:
a6 = -10
a10 = -26
We can use these values to find the common difference as follows:
a6 = a1 + (6 - 1) * d ----(1)
-10 = a1 + 5d
a10 = a1 + (10 - 1) * d ----(2)
-26 = a1 + 9d
Solving equations (1) and (2), we can find the values of a1 and d.
-10 = a1 + 5d ----(3)
-26 = a1 + 9d ----(4)
Subtracting equation (3) from equation (4), we get:
-26 - (-10) = (a1 + 9d) - (a1 + 5d)
-16 = 4d
d = -4
Now that we have the value of the common difference (d), we can find the value of the first term (a1) by substituting it into one of the equations:
-10 = a1 + 5d
-10 = a1 + 5(-4)
-10 = a1 - 20
a1 = 10 - 20
a1 = -10
Now we can find the 15th term (a15) using the formula:
an = a1 + (n - 1) * d
a15 = -10 + (15 - 1) * (-4)
a15 = -10 + 14 * (-4)
a15 = -10 + (-56)
a15 = -66
Therefore, the 15th term of the arithmetic progression is -66.
To find the 15th term of an arithmetic progression (AP) based on the given information, we need to determine the common difference (d) first. The common difference is the constant value added to each term to obtain the next term.
Given:
6th term (a6) = -10
10th term (a10) = -26
First, we can use the formula for the nth term of an AP:
an = a1 + (n - 1)d
where:
an = nth term of the AP
a1 = first term of the AP
d = common difference
n = number of terms
Using the information given, we can create two equations:
a6 = a1 + (6 - 1)d -> Equation (1)
-10 = a1 + 5d
a10 = a1 + (10 - 1)d -> Equation (2)
-26 = a1 + 9d
Now, we can solve these equations simultaneously. By subtracting Equation (1) from Equation (2), we can eliminate a1:
-26 - (-10) = (a1 + 9d) - (a1 + 5d)
-16 = 4d
Divide both sides by 4:
-16/4 = d
-4 = d
We found that the common difference (d) is -4.
Now, we can find the first term (a1) using Equation (1):
-10 = a1 + 5(-4)
-10 = a1 - 20
a1 = -10 + 20
a1 = 10
Now that we know the common difference (d = -4) and the first term (a1 = 10), we can find the 15th term (a15) using the formula:
a15 = a1 + (15 - 1)d
a15 = 10 + (15 - 1)(-4)
a15 = 10 + 14(-4)
a15 = 10 + (-56)
a15 = -46
Therefore, the 15th term of the arithmetic progression is -46.