Question

यदि किसी A.P. के पदों का योग Sn = (3n2-n) है, तो निम्न को ज्ञात करें
(i) प्रथम पद (ii) सार्व-अन्तर (iii) n वा पद ।

Answer 1

Step-by-step explanation:

Given यदि किसी A.P. के पदों का योग Sn = (3n2-n) है, तो निम्न को ज्ञात करें

(i) प्रथम पद (ii) सार्व-अन्तर (iii) n वा पद ।

• Given If in an A.P. The sum of the terms  is Sn = (3 n^2-n), then find the following.
• (i) first term (ii) common difference (iii) n term.
• Given Sn = 3 n^2 – n
• Now Sn-1 = 3(n – 1)^2 – (n – 1)
•                  = 3(n^2 – 2n + 1) – (n – 1)
•                  = 3n^2 – 6n + 3 – n + 1
•                  = 3n^2 – 7n + 4
• We need to find the n th term, so
• Sn – Sn-1 = 3n^2 – n – (3n^2 – 7n + 4)
•                = 3n^2 – n – 3n^2 + 7n – 4
•               = 6n – 4
• Now first term will be
• So an = 6(1) - 4
•          = 2
• Also common difference will be
• So an = 6n – 4
•    A2 = 6(2) – 4
•        = 12 – 4
•      = 8
• Now d = a2 – a1
•           = 8 – 2
• So d = 6

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