We are given that the first term of the arithmetic progression (AP) is 6 and the last term is 171. We know that the nth term of an AP is given by the formula:
an = a + (n-1)d
Where:
an is the nth term
a is the first term
d is the common difference
We can rewrite the formula as:
an = a + (n-1)(a - an)/n
Using the given values and solving for the common difference, we have:
171 = 6 + (14-1)(6 - 171)/14
170 = 13(165)/14
170 = 2145/14
14 * 170 = 2145
2380 = 2145
Now we can find the 16th term of the AP using the formula.
a16 = 6 + (16-1)(6 - 171)/14
a16 = 6 + 15(6 - 171)/14
a16 = 6 + 15(-165)/14
a16 = 6 - 2475/14
a16 = 6 - 175
a16 = -169
Therefore, the 16th term of the AP is -169.
The first term and the last term of an AP are 6 and 171 in that order. If there are 14th term find the 16th term of AP
1 answer