7. In an AP. ifS S 167 and S235, then find the sum of first 25 terms

1.	7. In an AP. ifS S 167 and S235, then find the sum of first 25 terms
Answer» Sn = n/2[2a + (n-1)d]S5 + S7 = 1675/2(2a + 4d) + 7/2(2a + 6d) = 16724a + 62d = 33412a + 31d = 167......... (1) S10 = 23510/2(2a + 9d) = 2352a + 9d = 47........... (2) Multiply eq(2) by 612a + 54d = 282......(3) Subtract eq(1) from eq(3)23d = 115d = 115/23 = 5 Put value of d in eq(1)12a + 31*5 = 16712a = 167 - 155a = 12/12 = 1 Then,AP is a, a+d, a+2d, a + 3d......1, 6, 11, 16, 21......

Answer»

Sn = n/2[2a + (n-1)d]S5 + S7 = 1675/2(2a + 4d) + 7/2(2a + 6d) = 16724a + 62d = 33412a + 31d = 167......... (1)

S10 = 23510/2(2a + 9d) = 2352a + 9d = 47........... (2)

Multiply eq(2) by 612a + 54d = 282......(3)

Subtract eq(1) from eq(3)23d = 115d = 115/23 = 5

Put value of d in eq(1)12a + 31*5 = 16712a = 167 - 155a = 12/12 = 1

Then,AP is a, a+d, a+2d, a + 3d......1, 6, 11, 16, 21......

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