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Answer :
The sum of 10 terms after excluding from the first and last term of the given AP. is: 1055
How to find the sum of an arithmetic sequence?
The formula for the sum of n terms of an arithmetic sequence is:
Sₙ = ⁿ/₂[2a + (n - 1)d]
Where:
n is number of terms
a is first term
d is common difference
There are 16 terms in the sequence and as such:
S₇ = ⁷/₂[2a + (7 - 1)d] = 126
⁷/₂[2a + 6d] = 126
7a + 21d = 126 ------(1)
Total sum of the last 7 terms is 441. Thus:
a + 9d + a + 10d + a + 11d + a + 12d + a + 13d + a + 14d + a + 15d = 441
7a + 84d = 441 ----(2)
Subtract eq 1 from eq 2 to get:
63d = 315
d = 315/63
d = 5
7a + 21(5) = 126
7a + 105 = 126
7a = 21
a = 3
The 16th term is:
3 + 15(5) = 78
Thus, the next ten terms are:
83, 88, 93, 98, 103, 108, 113, 118, 123, 128
Total = 83 + 88 + 93 + 98 + 103 + 108 + 113 + 118 + 123 + 128
Total = 1055
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