Question

There are 60 terms of an AP of which the first term is 8 and the last term is 185. What is the 31st term?

a) 92
b) 110
c) 120
d) 135

Answer 1

To find the 31st term of an arithmetic progression (AP), you can use the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference. Using the given information, we find that the 31st term is 98.

Step-by-step explanation:

To find the 31st term of an arithmetic progression (AP) when we know the first term, last term, and the number of terms, we can use the formula:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

Using the given information, we have a1 = 8, an = 185, and n = 60. Plugging these values into the formula, we get:

a31 = 8 + (31-1)d

Now, we can solve for d using the formula:

d = (an - a1) / (n-1)

Plugging in the values, we get:

d = (185 - 8) / (60-1) = 177 / 59

Now, we can substitute the value of d into the equation a31 = 8 + (31-1)d to find the 31st term:

a31 = 8 + (31-1)(177/59) = 8 + 30(3) = 8 + 90 = 98

Therefore, the 31st term of the AP is 98, which is not among the options provided.