The 14th term of an Ap is double the 4th term.find the 10th term if the 2nd term is 8
2nd term = 8 ----> a+d = 8 , #1
14th term is double the 4th term
a+13d = 2(a+3d)
a+13d = 2a + 6d
a - 7d = 0 , #2
#1 - #2:
8d = 8
d = 1
then a=7
term 10 = a+9d = 7 + 9 = 16
To find the 10th term of an arithmetic progression (AP), where the 14th term is double the 4th term and the 2nd term is 8, we need to first find the common difference (d).
We are given that the 2nd term is 8. We know that the 2nd term is given by the formula:
nth term = a + (n - 1)d
Substituting the given values, we have:
8 = a + (2 - 1)d
Simplifying the equation, we get:
8 = a + d
Now, we know that the 14th term is double the 4th term. Using the same formula, we have:
14th term = a + (14 - 1)d = 4th term × 2
Substituting the values, we get:
a + 13d = (a + 3d) × 2
Expanding the equation and simplifying, we have:
a + 13d = 2a + 6d
Rearranging the equation, we get:
a = 7d
Now, substitute this value of a in the equation we found earlier:
8 = 7d + d
Combining the terms and simplifying, we get:
8 = 8d
Dividing both sides by 8, we find:
d = 1
Now that we know the common difference (d = 1), we can find the 10th term using the formula:
10th term = a + (10 -1)d
Substituting the value of d and a from earlier, we have:
10th term = 7(1) + (10 -1)(1) = 7 + 9 = 16
Therefore, the 10th term of the AP is 16.