One of the most important question of ML Publication of Class10 of Arithmetic Progression Determine the AP whose third term is 16 and 7th term exceeds the 5th term by 12.
ML Publication, Class10, Chapter9, Arithmetic Progression, Question no. 13
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Determine the AP whose third term is 16 and 7th term exceeds the 5th term by 12.
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Let a be the First term, a3 be the third term, a5 be the 5th term and a7 be the 7th term
We know, an=a+(n−1)d
⇒ a3=16 [ Given ]
⇒ a+(3−1)d=16
⇒ a+2d=16 ……. (1)
⇒ Now, a7−a5=12 [ Given ]
⇒ [a+(7−1)d]−[a+(5−1)d]=12
⇒ 2d=12
∴ d=6
From equation (1), we get
a+2(6)=16
a+12=16
∴ a=4
So first term is 4
We can find AP by adding d continuously.
∴ Required AP is 4,10,16,22,28,34,40,......