Question

In an AP the 15th term is 12 and the sum of first 11 terms is 82 1/2 (means 82 and half). Find the first term and the common difference

Answer 1

HERE IT IS ;

→  A15 = 12

→A15 = A +14d

→A+14d = 12

→A = 12-14d      ----------1

NOW,

→Sn=n/2[2a +(n-1)d]

→S11 =11/2 [2a + 10d]

→but, S11 = 82.5

→82.5 = 11/2 [2(12-14d) + 10d ]

→82.5 ×2/11 = 24-28d +10d

→165/11 = 24-18d

→15 =24 - 18d

→15-24 = -18d

→-9 = -18d

∴d = 1/2

put d =1/2 in eq. 1

A =12+ 14d

A =12+ 14×1/2

A = 12+7

∴A = 19

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