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The 23rd term and 37th term of an AP are 54, 96 Find 30th term |
Answer» EXPLANATION.23rd term of an A.P. = 54. 37th term of an A.P. = 96. As we KNOW that, General term of an A.P. ⇒ Tₙ = a + (n - 1)d. ⇒ T₂₃ = a + (23 - 1)d. ⇒ T₂₃ = a + 22D. ⇒ a + 22d = 54. ⇒ (1) ⇒ T₃₇ = a + (37 - 1)d. ⇒ T₃₇ = a + 36d. ⇒ a + 36d = 96. ⇒ (2). From equation (1) & (2), we get. ⇒ a + 22d = 54. ⇒ a + 36d = 96. We get. ⇒ - 14d = - 42. ⇒ 14d = 42. ⇒ d = 42/14. ⇒ d = 3. Put the value of d = 3 in equation (1), we get. ⇒ a + 22d = 54. ⇒ a + 22(3) = 54. ⇒ a + 66 = 54. ⇒ a = 54 - 66. ⇒ a = -12. To FIND 30th term of an A.P.⇒ T₃₀ = a + (30 - 1)d. ⇒ T₃₀ = a + 29d. ⇒ T₃₀ = -12 + 29(3). ⇒ T₃₀ = -12 + 87. ⇒ T₃₀ = 75. MORE INFORMATION.Supposition of terms in A.P.(1) = Three terms as : a - d, a, a + d. (2) = Four terms as : a - 3d, a - d, a + d, a + 3d. (3) = Five terms as : a - 2d, a - d, a, a + d, a + 2d. |
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