The product of the first ten terms of PG(1,-2,4...)

To find the product of the first ten terms of the geometric progression with first term 1, common ratio -2, we can use the formula for the nth term of a geometric progression: an = a1 * r^(n-1) where a1 is the first term, r is the common ratio, and n is the term number. Substituting the given values into the formula, we get: a1 = 1 r = -2 The first ten terms of the geometric progression are: a1 = 1 a2 = -2 a3 = 4 a4 = -8 a5 = 16 a6 = -32 a7 = 64 a8 = -128 a9 = 256 a10 = -512 To find the product of these terms, we can multiply them together: 1 * (-2) * 4 * (-8) * 16 * (-32) * 64 * (-128) * 256 * (-512) = -137,438,953,472 Therefore, the product of the first ten terms of the geometric progression with first term 1, common ratio -2 is -137,438,953,472. To arrive at this answer, we used the formula for the nth term of a geometric progression to find the first ten terms of the sequence, and then we multiplied them together to find their product.