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Question
For an A.P., t17 = 54 and t9 = 30 find the first term(a) and common difference(d)
Solution
t17 = 54 and t9 = 30 ......[Given]
tn = a + (n – 1)d
t17 = 54
∴ a + (17 – 1)d = 54
∴ a + 16d = 54 ......(i)
t9 = 30
∴ a + (9 – 1)d = 30
∴ a + 8d = 30 ......(ii)
Subtracting equation (ii) from (i), we get
a + 16d = 54
a + 8d = 30
− − −
8d = 24
∴ d = `24/8` = 3
Substituting d = 3 in equation (ii), we get
a + 8(3) = 30
∴ a + 24 = 30
∴ a = 6
∴ first term (a) = 6 and common difference (d) = 3
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