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प्रश्न
Find the sum of all the 11 terms of an AP whose middle most term is 30.
उत्तर
Since, the total number of terms (n) = 11 ...[odd]
∴ Middle most term = `(n + 1)^("th")/2` term
= `((11 + 1)/2)^("th")` term
= 6th term
Given that,
a6 = 30 ...[∵ an = a + (n − 1)d]
⇒ a + (6 − 1)d = 30
⇒ a + 5d = 30 ...(i)
∵ Sum of n terms of an AP,
Sn = `n/2[2a + (n - 1)d]`
∴ S11 = `11/2[2a + (11 - 1)d]`
= `11/2(2a + 10d)`
= 11(a + 5d)
= 11 × 30 ...[From equation (i)]
= 330
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In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year. |
Based on the above information answer the following questions.
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- Find the production in the 12th year.
- Find the total production in first 10 years.
[OR]
In how many years will the total production reach 31200 cars?
