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Question
Find the sum of the A.P., 14, 21, 28, ......, 168.
Solution
Here a = 14 , d = 7 and tn = 168
tn = a + (n – 1)d
`=>` 168 = 14 + (n – 1)7
`=>` 154 = 7n – 7
`=>` 154 = 7n – 7
`=>` 161 = 7n
`=>` n = 23
We know that,
`S_n = n/2 [2a + (n - 1)d]`
`=> S_23 = 23/2 [2 xx 14 + (23 - 1)7]`
= `23/2 (28 + 154)`
= `23/2 xx 182`
= 2093
Therefore, the sum of the A.P., 14, 21, 28, ......, 168 is 2093.
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