The sum of 2nd term and 30th term of an arithmetic sequence is 50. Calculate the sum of first 31st term of this sequence
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The sum of 1st term and 31st term of the A.P is 50.
Step-by-step explanation:
Let the first term be 'a' and common difference be 'd'.
nth term of an A.P is given by,
Sum of 2nd and 30th term is 50.
a + (2 – 1)d + a + (30 – 1)d = 50
a + d + a + 29d = 50
2a + 30d = 50
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We've to find the sum of 1st and 31st terms.
= a + a + (31 – 1)d
= a + a + 30d
= 2a + 30d
= 50
Therefore, the sum of 1st term and 31st term of the A.P is 50.
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