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Oct 14, 2023 · a7 = a6 − a5 = −2 − (−1) = −1 a 7 = a 6 − a 5 = − 2 − (− 1) = − 1. a8 = a7 − a6 = −1 − (2) = 1 a 8 = a 7 − a 6 = − 1 − (2) = 1. . . . Therefore we see that the pattern repeats after every 6 terms. The sum of the first 6 terms = 2 + 1- 1 -2 -1 + 1 = 0. For every 6 terms, the sum = 0. 1000 = 996 + 4 = 6* (166) + 4.
Nov 1, 2023 · The sequence a1, a2, ..., an, ... is such that a1 = 3, a2 = 5, and an = an−1 − an−2 for all integers n ≥ 3. What is the sum of the first 100 terms of the sequence? (A) 2. (B) 3.
Apr 16, 2024 · Ex 5.3, 10 Show that a1, a2 … , an , … form an AP where an is defined as below (ii) an = 9 − 5n . Also find the sum of first 15 terms in each case Since an = 9 – 5n Hence, the series is 4, –1, –6, …….
Step 1: Identify the First Terms and Common Differences. Let the first term of both A.P.s (a1 and a2) be a1 = a2 = 72. Let the common difference of a1 be d1 and that of a2 be d2. According to the problem, d2 = d1 - 1. Step 2: Set Up the Sum of A.P. Formula.
If a 1, a 2,..., a n, are in AP with a common difference d ≠ 0, then the sum of the following series is (sin d) [cos e c a 1 cos e c a 2 + cos e c a 2 cos e c a 3 + ... + cos e c a (n - 1) cos e c a n] is equal to. A. s e c a 1 - s e c a n. B. c o t a 1 - c o t a n.
Numerical Estimation. Question. Download Solution PDF. Consider a sequence of numbers a 1, a 2, a 3, ….a n where a n = 1 n − 1 n + 2, for each integer (n > 0). What is the sum of the first 50 terms? This question was previously asked in. GATE CE 2018 Official Paper: Shift 1. Attempt Online. View all GATE CE Papers > (1 + 1 2) − 1 50.
The formula for an arithmetic sum is where is the first term, is the number of terms, and is the common difference. Now we use this formula to find a closed form for the first given equation and the sum of the given equations.
