"1. Let b1, b2, ...., b19 be the first 19 terms of an
arithmetic progression (AP) with b1+ b8 + b 12 +
b19 = 224. The sum of first 19 terms of the AP is
(1) 448
(2) 896
(3) 1064
(4) 1344
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b1, b2, b3, _ _ _, b19
are in A.P
b1 + b8 + b12 + b19 = 224
b1 = a
b8 = a + 7d
b12 = a + 11d
b19 = a + 18d
a + (a + 7d) + (a + 11d) + ( a + 18d) = 224
4a + 36d = 224
a + 9d = 56
a = 56 - 9d
sum of first 19 term
Sn = n/2 [ 2a + (n - 1) d ]
= 19/2 [ 2 ( 56 - 9d ) + (19 - 1) d ]
= 19/2 [ 112 - 18d + 18d ]
= 19 × 56
= 1064
option 3 is correct
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