What will be the sum of the first 18 terms of the series, if 7th and 17th terms are given

Question of The Day29-06-2020

If 7^th and 17^th terms of an arithmetic progression are 15 and 27, then what will be the sum of the first 18 terms of the series?

Answer

Correct Answer : d ) 324

Explanation :

We know that

nth term of an arithmetic progression is given as

a_n = a + (n – 1) d

where, a is the first term, d is the common difference

According to the question

a₇ = a + 6d = 15 ……. (1)

a₁₇ = a + 16d = 27 ……. (2)

Comparing equation (1) and (2) we get

a = 7.8 and d = 1.2

Thus,

Sum of an arithmetic progression is given as= \({n \over 2} (2a+(n-1)d)\)

Thus, sum of first 18 terms of the series will be

= \({18 \over 2} (2*7.8+(18-1)*1.2)\)

= 324

Hence, (d) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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