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CBSE Class 10 Answered

if s7=36 and s8=25 then a8=
Asked by kallutlabhagya123 | 14 Oct, 2020, 11:36: AM
answered-by-expert Expert Answer
It is assumed that this question is related to arithmetic progression. S7 means sum of first seven terms in arithmatic progression.
Similarly a8 means eighth term in arithmetic progression.
 
7 terms gives sum as 36 . 
If eigth term is added to above sum, we get sum of 8 terms as 25. 
 
Hence added eigth term = 36-25 = 11
 
Though above calculation is straight forward, we should know how to calculate a particular term in arithmetic progression 
by knowing sum of m terms and sum of n terms , were m and n can be any number.
Following method of finding calculation is used for this.
 
Sum of n-terms = Sn = (n/2) [ 2a + (n-1)d ] 
 
S7 = ( 7/2) [ 2a + 6d ] = 36   or   2a + 6d = 72/7  ................... (1)
S8 = ( 8/2) [ 2a + 7d ] = 25   or   2a + 7d = 25/4  ..................(2)
 
Hence eqn.(2) - eqn.(1) gives , d = (25/4) - (72/7) = -113/28
 
 by substituting d in eqn.(1), we get a = 17.25
 
Eighth term = a + 7d = 17.25 - [ 7 × 113/28 ] = -11
 
Answered by Thiyagarajan K | 14 Oct, 2020, 09:04: PM

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