$CATEGORY: Maths - TicTacLearn/5. Arithmetic progression/5. Arithmetic progression--Sum of First n Terms of an AP

//Multiple Choice

The sum of the first n terms of an AP is given by the formula\: {
= Sn \= n/2 × [2a+(n−1)d]
~ Sn \= a + (n−1)d
~ Sn \= n(a+d)
~ Sn \= n/2 × (a+n)
}

If the sum of the first 10 terms of an AP is 220 and the first term is 5, the common difference is\: {
~ 2
= 4
~ 6
~ 8
}

If the first term of an AP is 7, the common difference is 3, and n\=5 the sum of the first 5 terms is\: {
~ 55
~ 60
~ 50
= 45
}

In an AP, the sum of the first 20 terms is 210, and the first term is 5. The common difference is\: {
~ 0.5
= 1
~ 2
~ 3
}

The sum of the first n terms of the AP 2,4,6,8,...is\: {
~ Sn \= n/2 × (4n−2)
~ Sn \= n/2 × (n+4)
~ Sn \= n × (2n+2)
= Sn \= n/2 × (2n+2)
}

If the first term is a\=1 and the common difference d\=1, then the sum of the first n terms is\: {
~ n2+1
= n(n+1)/2
~ n(n−1)/2
~ n2/2
}

If the sum of the first n terms of an AP is 200, and n\=10, the average of the terms is\: {
~ 10
= 15
~ 20
~ 25
}

//True or False

The sum of the first n terms of an AP depends on the common difference. {T}

The sum of the first n terms of an AP is independent of the last term. {F}

For any AP, Sn  increases quadratically with n if d≠0 . {T}

If the common difference is zero, the sum of the first n terms is n×a . {T}

The sum of an AP is maximum when the common difference is maximum. {F}

If n\=1, the sum of the first n terms is equal to the first term. {T}

//Numericals



//Fill in the blanks

 In the formula
     Sn \= n/2 × [2a+(n−1)d]  the term d represents _______. {
     ~ Common ratio
     = Common difference
     ~ Last term
}

 If Sn\=100, n\=10, and a\=5, then d is _______. {
     ~ 1
     = 2
     ~ 3
}

 For the AP 3,7,11, the sum of the first 5 terms
     is _______. {
     = 35
     ~ 50
     ~ 60
}

 In an AP with the first term 8 and common difference 2, the sum of the first n terms is proportional to _______. {
     = n2
     ~ n
     ~ n/2
}

 If the sum of the first n terms is 36 and the first term is 4, the common difference is _______. {
     ~ 1
     = 2
     ~ 4
}

 The sum of an AP with equal terms is equal to _______. {
     = n×a
     ~ n/2 × a
     ~ n/2 × (a+l)
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=d in the formula -> Common difference
=Sequence with d\=0 -> Constant sequence
=Sum proportional to n2 -> Increasing AP
=AP with decreasing terms -> Negative common difference
=Sum of first term in AP -> Equal to first term
}



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