Question

the sum of 4th and 8th of an A.P term is 4 and sum of 6th and 10th term is 12 find first 3 term

Answer 1

Let the first term of an A.P = a and the common difference of the given  A.P = dAs we know that  a n = a+(n-1) d a 4 = a +( 4-1) d a 4 = a+3d Similarly ,  a 8 = a + 7 d a 6  = a + 5 d a 10 = a+ 9d Sum of 4 th and 8th terms of an A.P = 24 ( given ) a 4 +a 8 = 24 a + 3d + a + 7d = 24 2a + 10 d = 24 a +5d = 12  .....................(i) Sum of 6 th and 10 th term  of an A.P = 44 ( given ) a 6 +a 10 = 44 a + 5d +a+ 9d = 44 2a + 14 =44 a + 7d = 22  .....................(ii) Solving (i) & (ii)a +7 d  = 22 a + 5d = 12 -   -       -

2d  = 10 d = 5 From equation (i) ,  a + 5d = 12a + 5 (5) = 12 a+2 5= 12 a = - 13 a 2 = a+d = -13+5 = -8 a 3 = a 2 + d = -8+5 = -3 -13 ,-8,-3

Answer 2

Hey Friends,
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S4 = 2(2a + 3d ) = 4a + 12d
S8 = 4(2a + 7d ) = 8a + 28d
S6 = 3(2a + 5d ) = 6a + 15d
S10 = 5(2a + 9d) = 10a + 45d

A To questn

S4 + S8 = 4a + 12d + 8a + 28d
4 = 12a + 40d
4 = 4(3a + 10d)
1 = 3a + 10d ----------(1)

S6 + S10 =6a + 15d + 10a + 45d
12 = 16a + 60d
12 = 4(4a + 15d)
3 = 4a + 15 d ---------(2)