The first term of an AP is 4 and the sum of the first three...

The first term of an AP is 4 and the sum of the first three terms is 18. Find the product of the first three terms

Using the sum of an AP, S\(_n\) = \(\fra{n}{2}\) [ 2a + (n - 1)d]

S\(_3\) = \(\fra{3}{2}\) [ 2a + (3 - 1)d]

18 = \(\fra{3}{2}\) [ 2a + 2d]

2a + 2d = 12

a = 4

2(4) + 2d = 18 --> 8 + 2d = 12

2d = 4; d = 2

a = 4: a + d

= 4 + 2 = 6

a + 2d = 4 + 2]2]

= 8

product of the terms = 4 * 6 * 8 = 192

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