Question

an ap consists of 21 terms. the sum of the 3 terms in the middle is 129 and of the last 3 terms is 237. find the ap

Answer 1

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a.p. consists of 21 terms. the sum of the three terms in the middle is 129 and the sum of the last three terms is 237. find the first term and the common difference.

Report by Psatyam1918 21.12.2017

Answers

hukam0685p8u0ge

Hukam0685p8u0ge ★ Brainly Teacher ★

Dear Student,

Answer:

First term a =3

common difference d= 4.

Solution:

In an AP, nth term is given as Tn = a+ (n-1)d

n = 21

sum of last three terms i.e. T19, T20, T21

a + 18d + a + 19d + a + 20d = 237 \\ \\ 3a + 57d = 237 \\ \\ a + 19d = 79 \: \: \: \: \: \: eq1

sum of three middle terms T10,T11 and T12

a + 9d + a + 10d + a + 11d = 129 \\ \\ 3a + 30d = 129 \\ \\ a + 10d = 43 \: \: \: \: \: \: eq2

Subtract both equations

a + 19d - a - 10d = 79- 43 \\ \\ 9d =36 \\ \\ d = \frac{36}{9} \\ \\ d = 4 \\

Put the value of d, into eq 1 or eq2

a + 10d = 43 \\ \\ a + 40 = 43 \\ \\ a = 43 - 40 \\ \\ a = 3

So ,First term a =3

common difference d= 4.