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प्रश्न
Find the sum of the following arithmetic series:
`7 + 10 1/2 + 14 + ... + 84`
बेरीज
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उत्तर
The given arithmetic series is `7 + 10 1/2 + 14 + ... + 84`.
Here, `a = 7, d = 10 1/2 - 7 = 21/ 2 - 7 = (21 - 4)/2 = 7/2` and `l = 84.`
Let the given series contain n terms. Then,
an = 84
⇒ `7 + (n - 1) xx 7/2 = 84` ...[an = a + (n – 1)d]
⇒ `7/2 n + 7/2 = 84`
⇒ `7/2 n = 84 - 7/2 = 161/2`
⇒ `n = 161/7 = 23`
∴ Required sum = `23/2 xx (7 + 84)` ...`[S_n = n/2 (a + l)]`
= `23/2 xx 91`
= `2093/2`
= `1046 1/2`
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