Ultimate Trivia Quiz On Arithmetic Progression: Can You Pass?

Explanation
The given series starts with -10 and increases by 3 each time. To find the number of terms, we need to determine the value of the last term. We can find this by subtracting -10 from 50 and then dividing the result by 3. (-10 - 50) / 3 = 20. However, since the series includes both -10 and 50, we need to add 1 to the result. Therefore, the number of terms in the series is 20 + 1 = 21.

Explanation
The given arithmetic progression (AP) starts with 20 and has a common difference of -3. To find the 35th term, we can use the formula for the nth term of an AP: an = a1 + (n-1)d. Plugging in the values, we get a35 = 20 + (35-1)(-3) = 20 + 34(-3) = 20 - 102 = -82. Therefore, the 35th term of the AP is -82.

Explanation
The given arithmetic progression (AP) starts with 41 and each subsequent term is decreased by 3. To find the number of terms, we can use the formula for the nth term of an arithmetic progression: an = a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms. In this case, a = 41 and d = -3. We need to find the value of n when the last term, 8, is substituted into the formula. 8 = 41 + (n-1)(-3). Simplifying this equation, we get n = 12. Therefore, there are 12 terms in the given AP.

Explanation
To find the term of the arithmetic progression (AP) that is -81, we need to determine the common difference between the terms. By observing the given terms 21, 18, 15, ..., we can see that each term is decreasing by 3. Therefore, the common difference is -3. To find the 35th term, we can use the formula for the nth term of an AP: nth term = first term + (n-1) * common difference. Plugging in the values, we get 21 + (35-1) * (-3) = 21 + 34 * (-3) = 21 - 102 = -81. Hence, the 35th term is -81.

Explanation
The given arithmetic progression (AP) starts with 17 and has a common difference of -3. To find the 6th term from the end, we need to count 6 terms backwards from the last term (-40). Counting backwards, the last term is the 1st term from the end, the second last term is the 2nd term from the end, and so on. Therefore, the 6th term from the end is the 6th term in the AP, which is -40 + (6-1)(-3) = -40 + 15 = -25.

Explanation
The common difference of an arithmetic progression (AP) can be found by subtracting any two consecutive terms. In this case, the 5th term minus the 4th term gives us 3. This means that the common difference between each term is 3.

Explanation
The given arithmetic progression (AP) starts with 121 and decreases by 4 each time. To find the first negative term, we need to determine when the term becomes less than 0. By observing the pattern, we can see that the 32nd term is 121 - (4 * 31) = -3, which is the first negative term in the AP. Therefore, the 32nd term is the correct answer.

Explanation
To find the number of two-digit numbers that are divisible by 6, we need to determine the number of multiples of 6 between 10 and 99. The first multiple of 6 greater than 10 is 12, and the last multiple of 6 less than 100 is 96. To find the number of multiples, we can subtract the first multiple from the last multiple and divide by the common difference, which is 6. (96 - 12)/6 = 84/6 = 14. Therefore, there are 14 two-digit numbers divisible by 6.

Explanation
To find the value of p for which the numbers 2p - 1, 3p + 1, and 11 are in arithmetic progression (AP), we need to check if the common difference between consecutive terms is the same.

The common difference (d) can be calculated by subtracting the second term from the first term, or the third term from the second term.

In this case, we have:
(3p + 1) - (2p - 1) = 11 - (3p + 1)

Simplifying the equation:
p + 2 = 11 - 3p - 1
4p = 10
p = 2

Therefore, the value of p that satisfies the condition is p = 2.