The sum of 11 terms of an A. P is 891. Find the 28th and 45th terms if the common difference is 15
an = a1 + ( n - 1 ) d
a11 = a1 + ( 11 - 1 ) d
a11 = a1 + 10 d
Sn = n ( a1 + an ) / 2
S11 = 11 ( a1 + a11 ) / 2 = 891
11 ∙ ( a1 + a1 + 10 d ) / 2 = 891
11 ∙ ( 2 a1 + 10 d ) / 2 = 891
( 22 a1 + 110 d ) / 2 = 891
Multiply both sides by 2
22 a1 + 110 d = 1782
22 a1 + 110 ∙ 15 = 1782
22 a1 + 1650 = 1782
Subtract 1650 to both sides
22 a1 = 132
a1 = 132 / 22
a1 = 6
a28 = a1 + 27 d
a28 = 6 + 27 ∙ 15
a28 = 6 + 405
a28 = 411
a45 = a1 + 44 d
a45 = 6 + 44 ∙ 15
a45 = 6 + 660
a45 = 666