Question

For an A.P., t₁₇ = 54 and t₉ = 30 find the first term(a) and common difference(d)

Answer 1

t₁₇ = 54 and t₉ = 30    ......[Given]

t_n = 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