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प्रश्न
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n)..
Find:
- its first term and common difference
- sum of its first 25 terms
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उत्तर
Given, Tn = 6(7 – n)
a. For first term, put n = 1
Then, a1 = 6(7 – 1)
= 6 × 6
= 36
For second term, put n = 2
Then a2 = 6(7 – 2)
= 6 × 5
= 30
Then, common difference
∴ d = a2 – a1
= 30 – 36
= – 6
Hence, first term is 36 and common difference is - 6.
b. `S_n = n/2[2a + (n - 1)d]`
`S_25 = 25/2[2 xx 36 + (25 - 1)(-6)]`
= `25/2[72 - 144]`
= `25/2 xx (-72)`
S25 = – 900
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In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
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34 + 32 + 30 + ... + 10
Find the sum 25 + 28 + 31 + ….. + 100
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
Find the first term and common difference for the A.P.
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First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
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