Sequence

Algebra Level 1

The average of the first 5 terms in an arithmetic progression is 19 and the second term is 16. Find the sum of the common difference and the first term.


The answer is 16.

Stephen Liado by stephen liado , 21, Philippines

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2 solutions

Viki Zeta
Oct 3, 2016

Don't do too much calculations or process, answer is in the question itself.

2nd term is 16, a -> first term, d -> common difference a n = a + ( n − 1 ) d a 2 = a + ( 2 − 1 ) d = a + d a 2 = 16 a + d = 16 \text{2nd term is 16, a -> first term, d -> common difference} \\ a_n = a + (n-1)d\\ a_2 = a + (2-1)d = a + d \\ a_2 = 16 \\ a + d = 16

Therefore sum of first term and common-difference is 16 16

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By definition, the sum of the first term a 1 a_1 and common difference d d is the second term a 2 a_2 as a 2 = a 1 + d = 16 a_2 = a_1 + d = \boxed{16} .

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