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.

Let the first term of an A.P. be a and common difference be d. Given, ⇒ a 4 = 11 ⇒ a + (4 - 1)d = 11 ⇒ a + 3d = 11 .......(i) Also, ⇒ a 8 = 2a 4 + 5 ⇒ a + (8 - 1)d = 2[a + (4 - 1)d] + 5 ⇒ a + 7d = 2a + 6d + 5 ⇒ a - 2a + 7d - 6d = 5 ⇒ -a + d = 5 ........(ii) Adding (i) and (ii) we get, ⇒ a + 3d + (-a + d) = 11 + 5 ⇒ 4d = 16 ⇒ d = 4. Substituting value of d in (i) we get, ⇒ a + 3(4) = 11 ⇒ a + 12 = 11 ⇒ a = -1. A.P. = a, (a + d), (a + 2d), .......... = -1, 3, 7, ........... Hence, A.P. = -1, 3, 7, ........... and sum of first 50 terms = 4850.

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.

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

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k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is :
-2
0
2
3

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The sum of n terms of an A.P. is 3n². The second term of this A.P. is :
8
3
9
12

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Mathematics

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.

AP

Related Questions

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.

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

k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is :
-2
0
2
3

The sum of n terms of an A.P. is 3n². The second term of this A.P. is :
8
3
9
12

Mathematics

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.

AP

Related Questions

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.

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

k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is :-2023

The sum of n terms of an A.P. is 3n2. The second term of this A.P. is :83912

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.

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

k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is :
-2
0
2
3

The sum of n terms of an A.P. is 3n². The second term of this A.P. is :
8
3
9
12