Answer :
Final answer:
To find the sum of 10 terms after excluding the first and last terms of the given arithmetic progression (AP), first find the common difference of the AP. Then, use the formula for the sum of an arithmetic series to calculate the sum of the 10 terms.
Explanation:
To find the sum of 10 terms after excluding the first and last terms of the given arithmetic progression (AP), we need to first find the common difference of the AP. We can do this by subtracting the sum of the first 7 terms from the sum of the last 7 terms and dividing the result by 6 (since there are 6 terms between the first and last terms).
- Sum of first 7 terms = 126
- Sum of last 7 terms = 441
- Common difference = (Sum of last 7 terms - Sum of first 7 terms) / 6 = (441 - 126) / 6 = 315 / 6 = 52.5
Now that we know the common difference, we can calculate the sum of the 10 terms after excluding the first and last terms. First, we need to find the values of the second term (a2) and the 9th term (a9) using the formula:
an = a1 + (n-1)d
- a2 = a1 + d = 0 + 52.5 = 52.5
- a9 = a1 + (9-1)d = 0 + 8(52.5) = 420
Now, we can find the sum of the 10 terms using the formula for the sum of an arithmetic series:
Sn = n/2(a1 + an)
S10 = 10/2(0 + 420) = 2100
Learn more about Arithmetic Progressions here:
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