# If the 8th Term of an A.P is 37 and the 15th Term is 15 More than the 12th Term, Find the A.P. Also, Find the Sum of First 20 Terms of A.P. - Mathematics

Sum

If the 8th term of an A.P is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.

#### Solution

For an A.P

t_8 = 37

=> a + 7d = 37   ....(i)

Also t_15 - t_12 = 15

=> (a + 14d) - (a + 11d) = 15

=> a + 14d - a - 11d = 15

=> 3d = 15

=> d= 5

Subsituting d = 5 in (i) we get

a + 7 xx 5 = 37

=> a + 35 = 37

=> a = 2

∴ Required A.P = a, a +d, a + 2d, a + 3d, .....

= 2, 7, 12, 17, .....

Sum of the first 20 terms of this A.P = 20/2 [2 xx 2 + 19 xx 5]

= 10[4 + 95]

= 10 x 99

= 990

Concept: Arithmetic Progression - Finding Sum of Their First ‘N’ Terms.
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 10 Arithmetic Progression
Exercise 10 (C) | Q 11 | Page 144