Find the sums given below : (i) 7 +10(1/2)+14+...+84 (ii) 34 + 32 + 30 + ....... + 10 (iii) -5 + (-8) + (-11) + ...... + (-230)

Question

KnowledgeBoat · Accepted Answer

(i) Given, ⇒ ⇒ 7 + 10.5 + 14 + ......... + 84 The above sequence is an A.P. with first term (a) = 7 and common difference (d) = 10.5 - 7 = 3.5 Let nth term be 84. By formula, a_n = a + (n - 1)d Substituting values we get : ⇒ 84 = 7 + (n - 1)(3.5) ⇒ 84 = 7 + 3.5n - 3.5 ⇒ 84 = 3.5n + 3.5 ⇒ 3.5n = 84 - 3.5 ⇒ 3.5n = 80.5 ⇒ n = = 23. By formula, S_n = Substituting values we get : Hence, sum = . (ii) Given, 34 + 32 + 30 + ....... + 10 The above sequence is an A.P. with first term (a) = 34 and common difference (d) = 32 - 34 = -2. Let nth term be 10. By formula, a_n = a + (n - 1)d Substituting values we get : ⇒ 10 = 34 + (n - 1)(-2) ⇒ 10 = 34 - 2n + 2 ⇒ 10 = 36 - 2n ⇒ 2n = 36 - 10 ⇒ 2n = 26 ⇒ n = = 13. By formula, S_n = Substituting values we get : Hence, sum = 286. (iii) Given, -5 + (-8) + (-11) + ....... + (-230) The above sequence is an A.P. with first term (a) = -5 and common difference (d) = -8 - (-5) = -8 + 5 = -3. Let nth term be -230. By formula, a_n = a + (n - 1)d Substituting values we get : ⇒ -230 = -5 + (n - 1)(-3) ⇒ -230 = -5 - 3n + 3 ⇒ -230 = -3n - 2 ⇒ 3n = -2 + 230 ⇒ 3n = 228 ⇒ n = = 76. By formula, S_n = Substituting values we get : Hence, sum = -8930.

Mathematics

Find the sums given below : (i) 7 +10(1/2)+14+...+84 (ii) 34 + 32 + 30 + ....... + 10 (iii) -5 + (-8) + (-11) + ...... + (-230)

AP

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Mathematics

Find the sums given below : (i) 7 +10(1/2)+14+...+84 (ii) 34 + 32 + 30 + ....... + 10 (iii) -5 + (-8) + (-11) + ...... + (-230)

AP

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