Answer :
Final answer:
To find the sum of the first 16 terms of an arithmetic progression, use the formula Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
Explanation:
To find the sum of the first 16 terms of the arithmetic progression (AP), we can use the formula for the sum of an AP:
Sn = (n/2)(2a + (n-1)d)
Where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
In this case, we know that the sum of the first 4 terms is 56 cm, so S4 = 56. We also know that the first term a is 176. We can substitute these values into the formula and solve for the sum of the first 16 terms:
S16 = (16/2)(2(176) + (16-1)d) = 8(352 + 15d)
Since we don't know the common difference d, we can't find the exact value of the sum. We can, however, eliminate answer choices that are not multiples of 8, since the sum must be a multiple of 8. Therefore, the correct answer is option a) 1008 cm.
