If the 8 th term of an A.P. is 37 and the 15 th term is 15 more than the 12 th term, find the A.P. Also, find the sum of first 20 terms of this A.P.

Given, ⇒ a 8 = a + (8 - 1)d ∴ a + 7d = 37 ........(i) Also, ⇒ a 15 = a 12 + 15 ⇒ a + (15 - 1)d = a + (12 - 1)d + 15 ⇒ a + 14d = a + 11d + 15 ⇒ a - a + 14d - 11d = 15 ⇒ 3d = 15 ⇒ d = 5. Substituting value of d in (i) we get, ⇒ a + 7(5) = 37 ⇒ a + 35 = 37 ⇒ a = 2. A.P. = a, (a + d), (a + 2d), .......... = 2, 7, 12, ........... Hence, A.P. = 2, 7, 12, ........... and sum = 990.

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

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In an A.P. the first term is 25, n^th term is -17 and the sum of n terms is 132. Find n and the common difference.

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The sum of n natural numbers is 5n² + 4n. Find its 8^th term.

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The fourth term of an A.P. is 11 and the eight term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.

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Mathematics

If the 8^th term of an A.P. is 37 and the 15^th term is 15 more than the 12^th term, find the A.P.
Also, find the sum of first 20 terms of this A.P.

AP

Related Questions

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

In an A.P. the first term is 25, n^th term is -17 and the sum of n terms is 132. Find n and the common difference.

The sum of n natural numbers is 5n² + 4n. Find its 8^th term.

The fourth term of an A.P. is 11 and the eight term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.

Mathematics

If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P.Also, find the sum of first 20 terms of this A.P.

AP

Related Questions

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

In an A.P. the first term is 25, nth term is -17 and the sum of n terms is 132. Find n and the common difference.

The sum of n natural numbers is 5n2 + 4n. Find its 8th term.

The fourth term of an A.P. is 11 and the eight term exceeds twice the fourth term by 5. Find the A.P. and the sum of first 50 terms.

If the 8^th term of an A.P. is 37 and the 15^th term is 15 more than the 12^th term, find the A.P.
Also, find the sum of first 20 terms of this A.P.

In an A.P. the first term is 25, n^th term is -17 and the sum of n terms is 132. Find n and the common difference.

The sum of n natural numbers is 5n² + 4n. Find its 8^th term.