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Answer :
Final answer:
The sum is 2464
Explanation:
Let's assume that the first term of the AP is 'a' and the common difference is 'd'.
The sum of the first four terms of the AP is given as 56 cm:
a + (a + d) + (a + 2d) + (a + 3d) = 56
4a + 6d = 56
The 8th term of the AP is given as 176 cm:
a + 7d = 176
Solving these two equations, we find a = 4 and d = 20.
To find the sum of the first 16 terms of the AP, we can use the formula for the sum of an AP:
Sum = (n/2)(2a + (n - 1)d)
Substituting n = 16, a = 4, and d = 20 into the formula:
Sum = (16/2)(2(4) + (16 - 1)(20)) = 8(8 + 300) = 8(308) = 2464 cm
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