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if s7=36 and s8=25 then a8=
Asked by kallutlabhagya123 | 14 Oct, 2020, 11:36: AM
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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