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प्रश्न
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
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उत्तर
We have been given an A.P
2+6+10+...+x=1800
a = 2, d = 6 - 2 = 4, `a_n = x "and" s_n = 1800`
Firstly, we will find using
`S_n = n/2[2a + (n - 1)d]`
`1800 = n/2[2 xx 2 + (n - 1)4]`
`1800 = (4n + 4n^2 - 4n)/2`
`900 = n^2`
⇒ n = ±30
Number of terms can not be negative
n = 30
Now for value of x which is `a_n`
`a_n = a + (n - 1)d`
`x = 2 + (30 - 1)4`
x = 2 + 116
x = 118
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