Question

the 4th term of an ap is 3 times the first term and 7th term exceed twice the 3rd term by 1 find the first term and common difference​

Answer 1

Answer:

a = 3, d = 2

Step-by-step explanation:

Given

T4 = 3T1

T7 = 2T3 + 1

according to Tn = a+(n-1)d

T4 = a + 3d

T1 = a

T7 = a+6d

T3 = a+2d

now from given,

T4 = 3T1

a+3d = 3(a)

3d = 2a

d = 2/3 a

T7 = 2T3 + 1

a+6d = 2(a+2d) + 1

a+6d = 2a+4d + 1

2d= a + 1

2(2/3)a= a + 1

4/3a= a + 1

a/3 = 1

a = 3

substitute a = 3 in d = 2/3 a

then,d= 2

Hope it helped

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