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Question
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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Solution
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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