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प्रश्न
An AP 8, 10, 12, … has 60 terms. Find its last term. Hence, find the sum of its last 10 terms.
उत्तर
The given AP is 8, 10, 12,……
Here , a = 8 , d = 10-8=2 and n = 60
Since there are 60 terms in the AP, so the last term of the AP is a60 .
l = a60 = 8 + (60-1) × 2 [an = a +(n-1) d]
= 8+118
=126
Thus, the last term of the AP is 126.
Now,
Sum of the last 10 terms of the AP
= S60 - S50
`= 60/2 [ 2 xx 8 +(60-1) xx2 ] - 50/2 [ 2xx 8 + (50-1) xx2]`
`{S_n = n/2 [ 2a + (n-1) d]}`
=30 × (16+118 ) -25 × (16+98)
= 30 × 134 - 25 × 114
= 4020 - 2850
= 1170
Hence, the required sum is 1170.
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