Author: Imad Ali

Correct Answer: C. 3160

The given series is an arithmetic progression with the first term (a) being 1 and the common difference (d) being 4.

To find the sum of the series up to the 40th term, we can use the formula for the sum of an arithmetic progression:

S = (n/2) x [2a + (n-1)d]

where S is the sum of the series, n is the number of terms in the series, a is the first term, and d is a common difference.

Substituting the values into the formula, we get:

S = (40/2) x [2(1) + (40-1)(4)] S = 20 x [2 + 39(4)] S = 20 x 158 S = 3,160

Therefore, the sum of the series 1, 5, 9, 13, …, up to the 40th term is 3,160.

Correct Answer: A. -75 

The given series is an arithmetic progression with the first term (a) being -15 and the common difference (d) being the difference between consecutive terms which is -22 – (-15) = -7.

To find the 11th term of the series, we can use the formula:

an = a + (n-1)d

where an is the nth term of the series, n is the number of the term we want to find, a is the first term, and d is a common difference.

Substituting the values into the formula, we get:

a11 = -15 + (11-1)(-7) a11 = -15 – 60 a11 = -75

Therefore, the 11th term of the series is -75.

Correct Answer: C. X

Here, the two numbers are x-3 and x+3. Therefore, the A.M between them is:

A.M = (x-3 + x+3)/2

Simplifying this expression, we get:

A.M = (2x)/2

A.M = x

Therefore, the arithmetic mean between x-3 and x+3 is simply x.

Correct Answer: B. Common difference

A sequence is called arithmetic if there is a constant difference between consecutive terms. In other words, if the difference between any two consecutive terms is the same throughout the sequence, then it is called an arithmetic sequence.

For example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence because the difference between any two consecutive terms is 3.

The general formula for the nth term of an arithmetic sequence is:

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 between consecutive terms.