Question
Download Solution PDFFind the sum of the first 157 terms of an AP whose first term and third term are 160 and 170 respectively.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
First term (a) = 160
Third term = 170
Total terms (n) = 157
Formula Used:
Sum of first n terms of an AP (Sn) = n/2 × [2a + (n - 1) × d]
Common difference (d) = (Third term - First term) / (3 - 1)
Calculation:
d = (170 - 160) / 2
⇒ d = 10 / 2
⇒ d = 5
S157 = 157/2 × [2 × 160 + (157 - 1) × 5]
⇒ S157 = 157/2 × [320 + 156 × 5]
⇒ S157 = 157/2 × [320 + 780]
⇒ S157 = 157/2 × 1100
⇒ S157 = 157 × 550
⇒ S157 = 86350
The sum of the first 157 terms is 86350.
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