First term of an arithmetic progression is 23 and the sum of first 10 terms is 725, then find the 4^th term of that arithmetic progression.

GIVEN:

First term of an arithmetic progression is 23 and the sum of first 10 terms is 725.

CONCEPT:

Arithmetic progression formulas for calculating n^th term and sum of ‘n’ terms.

FORMULA USED:

n^th term of an arithmetic progression = [a + (n - 1) × d]

Sum of ‘n’ terms of an arithmetic progression = n / 2 × [2a + (n - 1) × d]

Where

a = first term, d = common difference, n = number of terms

CALCULATION:

Using the formula:

10 / 2 × [2 × 23 + (10 - 1) × d] = 725

⇒ 5 × [46 + 9d] = 725

⇒ 9d = 99

⇒ d = 11

Now,

4^th term = 23 + (4 - 1) × 11

⇒ 23 + 33

⇒ 56

∴ Forth term of given AP is 56