$4^{t h}$ term of an A. P. is equal to 3 times its first term $7^{t h}$ term exceeds twice the $3^{r d}$ term by 1. Find the first term and the common difference.

Open in App

Solution

Given $a_{4} = 3 a_{1} i . e, (a + 3 d) = 3 a H e n c e, 2 a = 3 d ∴, a = \frac{3 d}{2} A l s o g i v e n t h a t a_{7} = 2 a_{3} + 1 (a + 6 d) = 2 (a + 2 d) + 1 a + 6 d = 2 a + 4 d + 1 a = 2 d - 1 \frac{3 d}{2} = 2 d - 1 \frac{d}{2} = 1 ∴, d = 2 a = \frac{3 d}{2} = 3$

Suggest Corrections

Similar questions

Q. The

4^{t h}

term of an A.P. is three times the first and the

7^{t h}

term exceeds twice the third term by

1

. Find the first term and the common difference.

$4^{t h}$ term of an AP is equal to 3 times the first term and $7^{t h}$ term exceeds twice the 3rd term by $1.$ Find the first term and the common difference.

Q. The fourth term of an A.P is equal to

3

times the first term, and the seventh term exceeds twice the

3^{r d}

term by

1

. Find the first term and the common difference.

The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1, find the first term and the common difference.

Q. The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.

Join BYJU'S Learning Program

4th term of an A. P. is equal to 3 times its first term 7th term exceeds twice the 3rd term by 1. Find the first term and the common difference.

Given a4=3a1i.e,(a+3d)=3aHence,2a=3d∴,a=3d2Also given that a7=2a3+1(a+6d)=2(a+2d)+1a+6d=2a+4d+1a=2d–13d2=2d–1d2=1∴,d=2a=3d2=3

$4^{t h}$ term of an A. P. is equal to 3 times its first term $7^{t h}$ term exceeds twice the $3^{r d}$ term by 1. Find the first term and the common difference.

Given $a_{4} = 3 a_{1} i . e, (a + 3 d) = 3 a H e n c e, 2 a = 3 d ∴, a = \frac{3 d}{2} A l s o g i v e n t h a t a_{7} = 2 a_{3} + 1 (a + 6 d) = 2 (a + 2 d) + 1 a + 6 d = 2 a + 4 d + 1 a = 2 d - 1 \frac{3 d}{2} = 2 d - 1 \frac{d}{2} = 1 ∴, d = 2 a = \frac{3 d}{2} = 3$