The 14th term of an A.P is 864,while 25th term is 1557 find the ,19th term,sum of 13th and 56th terms,product of 6th and 13th terms.

Answer 1

a14 = a1 + 13 d = 864

a25 = a1 + 24 d = 1557

a25 - a14

a1 + 24 d = 1557
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a1 + 13 d = 864
____________
11 d = 693

d = 693 / 11

d = 63

Replace this value in equation:

a1 + 13 d = 864

a1 + 13 ∙ 63 = 864

a1 + 819 = 864

a1 = 864 - 819

a1 = 45

a19 = a1 + 18 d = 45 + 18 ∙ 63 = 45 + 1134 = 1179

a6 = a1 + 5 d = 45 + 5 ∙ 63 = 45 + 315 = 360

a13 = a1 + 12 d = 45 + 12 ∙ 63 = 45 + 756 = 801

a56 = a1 + 55 d = 45 + 55 ∙ 63 = 45 + 3465 = 3510

a13 + a56 = 801 + 3510 = 4311

a6 ∙ a13 = 360 ∙ 801 = 288360