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in Arithmetic Progression by (41.6k points)
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If the sum of first 7 terms and 15 terms of an A.P. are 98 and 390 respectively, then find the sum of first 10 terms.

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Sum of the first 7 terms of AP = 98 

\(\frac{7}{2}\)[2a + (7-1)d] = 98 

2a + 6d = 98 × \(\frac{2}{7}\)

2a + 6d = 28 

a + 3d = 14 ……………..(1)

Sum of the first 15 terms of AP = 390 

\(\frac{15}{2}\) [2a + (15 – 1)d] = 390 

2a + 14d = 390 × \(\frac{2}{15}\)

2a + 14d – 52 

a + 7d = 26 ……………(2) 

by solving (1) and (2) 

a = 5 and d = 3 

Sum of the first 10 terms 10 

\(\frac{10}{2}\) [2a + (10 – 1)d] 

– 5[2(5) + 9(3)] 

= 5[10 + 27] 

= 5 × 37 = 185

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