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CBSE Class 10 Answered

The sum of the first 7 terms of an AP is 63 and that of its next 7 terms is 161.find the AP
Asked by prassanna.j | 13 Nov, 2023, 11:24: PM
answered-by-expert Expert Answer
Let a be the first term of Aritnmetic Progression(AP) and d be the common difference of AP
 
Sum of n-terms of AP  is 
 
begin mathsize 14px style n over 2 open square brackets 2 a space plus space left parenthesis n minus 1 right parenthesis d close square brackets space equals space S subscript n end style
 
If sum of first 7 terms is 63 , then we have
 
begin mathsize 14px style 7 over 2 open square brackets 2 a space plus space 6 d close square brackets space equals space 63 end style
 
By simplifying above expression, we get
 
begin mathsize 14px style a space plus space 3 space d space equals space 9 end style ........................... (1)
 
If sum of next 7 terms is 161 , then sum of first 14 terms is ( 63+161) = 224
 
Hence , expression for sum of 14 terms is
 
begin mathsize 14px style 14 over 2 open square brackets 2 space a space plus space 13 space d close square brackets space equals space 224 end style
begin mathsize 14px style 2 space a space plus space 13 space d space equals 32 space end style........................... (2)
 
By solving eqn.(1) and eqn.(2) ,  we get  a = 3 and d = 2
 
Hence AP is  3 , 5, 7, 9 ..........................
Answered by Thiyagarajan K | 14 Nov, 2023, 10:51: AM

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