Solve the equation 1 4 7 10 x 287
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Solve the solution 1+4+7+10.............+x = 287
Answered by admin @
Answer:
Step-by-step explanation:
Solution :-
Here, a = 1,
and d = 4 - 1 = 2,
S(n) = n
Let n be the number of terms.
We know that,
S(n) = n/2[2a + (n - 1)d]
Putting all the values, we get
⇒ 287 = n/2[2 × 1 + (n - 1) (3)]
⇒ 287 = n/2[2 + (n - 1)3]
⇒ 574 = 3n² - n
⇒ 3n² - n - 574 = 0
⇒ 3n² - 42n + 41n - 574 = 0
⇒ 3n(n - 14) + 41(n - 14) = 0
⇒ n = 14, - 41/3 (As n can't be negative)
⇒ n = 14
We know that,
a + (n - 1)d = x
⇒ 1 + (14 - 1) (3) = 3
⇒ 1 + 13 (3) = 3
⇒ x = 40.
Hence, the value of x is 40.
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