The 4th term of an Ap is 11. The sum of fifth and seventh terms of the A.P is 34.Find the (i) The First Term
(ii)common difference (iii) A.P
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Step-by-step explanation:
a4 = 11
[a+(4-1)d] = 11
a + 3d = 11
a = 11-3d_______(1)
a5 + a7 = 34
[a+(5-1)d] + [a+(7-1)d] = 34
(a+4d) + (a+6d) = 34
a + 4d + a + 6d = 34
2a + 10d = 34
Putting value of a
2(11-3d) + 10d = 34
22 - 6d + 10d = 34
22 + 4d = 34
4d = 34-22
4d = 12
d = 12/4 = 3
a = 11 - 3d
a = 11-3×3
a = 11-9 = 2
(i) a(First term) = 2
(ii) d(Common difference) = 3
(iii) A.P = 2, 5, 8, 11,_______
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