$CATEGORY: Maths - TicTacLearn/5. Arithmetic progression/5. Arithmetic progression--Arithmetic Progression

//Multiple Choice

An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is\: {
= Constant
~ Increasing
~ Decreasing
~ None of these
}

In the AP 5, 8, 11, 14, ..., the common difference is\: {
= 3
~ 5
~ 8
~ 2
}

If the first term of an AP is 7 and the common difference is 4, the second term is\: {
~ 7
= 11
~ 14
~ 10
}

The nth term of an AP is given by the formula\: {
= a+(n−1)d
~ a−(n−1)d
~ a×(n−1)d
~ a/(n−1)d
}

If the nth term of an AP is 23, the first term is 5, and the common difference is 3, the value of n is\: {
~ 5
~ 7
~ 8
= 6
}

In an AP, the sum of the first n terms is given by\: {
= n/2×[2a+(n−1)d)]
~ n×a+d
~ n×a/d
~ None of these
}

If the terms of an AP are 2, 4, 6, 8, ..., the common difference is\: {
= 2
~ 4
~ 6
~ 8
}

If the common difference of an AP is 0, then the AP is\: {
~ Increasing
= Constant
~ Decreasing
~ None of these
}

//True or False

An arithmetic progression has a variable common difference. {F}

The nth term of an AP is always greater than the first term. {F}

The common difference of an AP can be negative. {T}

The sum of the first n terms of an AP is independent of the common difference. {F}

All terms in an AP with zero common difference are equal. {T}

If a\=5 and d\=3, the second term of the AP is 8. {T}

If a\=2, d\=4, and n\=5, the fifth term of the AP is 18. {T}

The sequence 5, 10, 15, 20, ... is not an AP. {F}

//Numericals



//Fill in the blanks

The common difference in an arithmetic progression is always _______. {
= Constant
~ Variable
~ Increasing
}

The first term of an AP is denoted by _______. {
~ d
= a
~ n
}

If the common difference of an AP is negative, the terms of the AP will _______. {
~ Increase
= Decrease
~ Remain the same
}

In the AP 3, 6, 9, 12, ..., the common difference is _______. {
= 3
~ 6
~ 9
}

In an AP, if the common difference is zero, then all terms are _______. {
~ Different
= Same
~ Increasing
}

The formula to calculate the sum of the first n terms of an AP is Sn \= n/2 [(2a + (n - 1) x _____________). {
~ Common ratio
= Common difference
~ Number of terms
}

The sequence 7, 14, 21, 28, ... is an AP with common differences _______. {
= 7
~ 14
~ 21
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=First term of an AP -> a
=Common difference -> d
=nth term of an AP -> a+(n−1)d
=AP with zero common difference -> Constant sequence
}



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