The first twelfth and last term of an A.p an 43½ and 376½ respectively determine,the number of term in the sequence,the sum of all the term,the 8oth term?
To find the number of terms in the arithmetic progression (AP), we can use the formula:
Number of terms (n) = (last term - first term) / common difference + 1
Given that the first term is 43½ and the last term is 376½, we can substitute these values into the formula:
n = (376½ - 43½) / d + 1
To find the common difference (d), we can use the formula:
d = (last term - first term) / (n - 1)
Given that the first term is 43½, the last term is 376½, and n is the number of terms, we can substitute these values into the formula to find the common difference:
d = (376½ - 43½) / (n - 1)
To find the sum of all the terms in the AP, we can use the formula:
Sum = n/2 * (first term + last term)
Given that the first term is 43½, the last term is 376½, and n is the number of terms, we can substitute these values into the formula to find the sum of all the terms:
Sum = n/2 * (43½ + 376½)
Now, to find the 80th term in the AP, we can use the formula:
An = first term + (n - 1) * d
Given that the first term is 43½, n is 80, and d is the common difference, we can substitute these values into the formula to find the 80th term:
A80 = 43½ + (80 - 1) * d
With these formulas, we can calculate the number of terms, the sum of all the terms, and the 80th term in the arithmetic progression.