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Question
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
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Solution
For this A.P.,
a = 7
l = 84
d = a2 − a1
= `10 1/2 - 7`
= `21/2 - 7`
= `7/2`
Let 84 be the nth term of this A.P.
l = a (n - 1)d
`84 = 7 + (n - 1) × 7/2`
`77 = (n - 1) × 7/2`
22 = n − 1
n = 23
We know that,
Sn = `n/2 (a + l)`
S23 = `23/2 [7 + 84]`
= `23/2xx91`
= `2093/2`
= `1046 1/2`
Thus, the required sum is `1046 1/2`.
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