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
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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.

KnowledgeBoat · Accepted Answer

Let the first term of an A.P. be a and common difference be d. Given, ⇒ a₄ = 11 ⇒ a + (4 - 1)d = 11 ⇒ a + 3d = 11 .......(i) Also, ⇒ a₈ = 2a₄ + 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.

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

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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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