Multiple choice

Find the first term of the AP series in which 10th term is 6 and 18th term is 70?

  1. 76

  2. -76

  3. 66

  4. -66

  5. 0
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D Correct answer
Explanation

a + 9d = 6, a + 17d = 70. Subtracting: 8d = 64, so d = 8. a + 9(8) = 6 => a + 72 = 6 => a = -66.

AI explanation

In an arithmetic progression, the nth term is calculated using the formula a plus the quantity of n minus 1 multiplied by d. Subtracting the 10th term from the 18th term gives 70 minus 6, which equals 64, and this represents the common difference multiplied by 8. Dividing 64 by 8 gives the common difference as 8. Substituting this back into the 10th term formula gives 6 equals a plus 9 multiplied by 8, which simplifies to a equals 6 minus 72. Therefore, the first term of the series is minus 66.

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