Q. 2 A

Find the sum of the following:

3 + 11 + 19 + … + 803

Answer :

The arithmetic progression 3, 11, 19, …., 803 is given.
Here first term is 3 and common difference is 11 – 3 = 8.
Last term l = 803


Let no. of terms be n.
So, an = a + (n - 1)d


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



803 = 3 + (n - 1) × 8
800 = (n - 1) × 8
100 = n – 1
n = 101


Since the sum of n terms is
Sn =


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



So sum of 101 terms S101
]
= 50.5[ 6 + 100×(8)]
= 50.5[ 6 + 800]
= 50.5 × (806)
= 40703


Hence, Sum is 40703.


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