Why is the important to understand the given sequence and identify the first term, common difference and the number of terms before applying the formula.
How to find the sum of the given sequence.
Important NCERT Questions, Class 10.
Find the sums given below : 7 + 10(1/2) + 14 + … + 84
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Here, a = 7 and d = 10(1/2) – 7 = 21/2 – 7 = 7/2.
Let, the nth term of the A.P. is 84.
Therefore, a_n = 84
⇒ a + (n -1)d = 84
⇒ 7 + (n – 1)(7/2) = 84
⇒ (n – 1)(7/2) = 77
⇒ n – 1 = 22
⇒ n = 23
The sum of n terms of an AP is given by
S_n = n/2[a +l]
⇒ S₂₃ = 23/2[7 + 84]
⇒ S₂₃ = 23/2[91] = 2093/2 = 1046 (1/2)