Question

3 + 8 +13 + ... + x = 1974.

x is​

Answer 1

3+8+13+...+x=1974

x is 138

Answer 2

Solution :-

→ First term = a = 3

→ Common difference = d = 8 - 3 = 5

→ S(n) = 1974 .

So,

→ S(n) = (n/2)[2a + (n - 1)d]

→ 1974 = (n/2)[2*3 + (n - 1)5]

→ 3948 = n(6 + 5n - 5)

→ 3948 = 5n² + n

→ 5n² + n - 3948 = 0

→ 5n² - 140n + 141n - 3948 = 0

→ 5n(n - 28) + 141(n - 28) = 0

→ (n - 28)(5n + 141) = 0

→ n = 28 or (-141/5)

→ n = 28 .

therefore,

→ T(n) = a + (n - 1)d

→ x = 3 + 27 * 5

→ x = 3 + 135

→ x = 138 (Ans.)

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