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Question
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
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Solution
Let there be n terms in this A.P.
First term a = 34
Common difference d = 18
Last term l = 700
`=>` a + (n – 1)d = 700
`=>` 34 + (n – 1) × 18 = 700
`=>` (n – 1) × 18 = 666
`=>` n – 1 = 37
`=>` n = 38
Sum of first n terms = `n/2 [a + l]`
= `38/2 [34 + 700]`
= 19 × 734
= 13946
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